Solve the right triangle below. Find the measure of the indicated angle to the nearest degree. For the given series, find its sum, if it converges. Two ships, the Queen Elizabeth and the Queen Mary are 35 km apart. Solve the following. Questions on Amplitude, Period, range and Phase Shift of Trigonometric Functions, Questions on Complementary and Supplementary Angles, Questions on Converting Angles to Degrees and Radians, Questions on Unit Circles in Trigonometry, Questions on Graphs of Trigonometric Functions, Questions on Solving Simple Trigonometric Equations, Questions on Using Symmetry of Unit Circles in Trigonometry, Questions on Trigonometric Functions of Multiple Angles, Trigonometry Problems and Questions with Solutions - Grade 10, Trigonometry Problems and Questions with Solutions - Grade 12. If the angle of depression from the top of the tower to the point where the cable meets the ground is... A pilot in an airplane flying at 25,000 ft sees two towns directly ahead of her in a straight line. Assume that two stars are in circular orbits about a mutual center of mass and are separated by a distance a. If sinBeta = k, which of the following could be the value of Beta? Show that the relation between the horizontal and vertical components of the balls position is given by y=L-\sqrt{(L^2 - x^2)}. The tower of a tower crane casts a shadow (on level ground) of 25 m when the sun is 72 degree above the horizon. 16 18x2 29 15 23 lix 370 14x—3 1. The buildings are 30 m apart. Solve, finding all exact solutions in [0, 2\pi). A. Find all exact solutions on the interval 0 less than or equal to theta less than or equal to 2 pi. Use special right triangles to find the value of v A. Infinitely many B. sin (theta)/1-cos^2 (theta) = csc (theta), Verify the identity. At the time of the punt A.J. -2 B. A 5 ft tall girl stands on level ground the sun is 25 degrees above the horizon. Show that in any triangle ABC we have: b cos C + c cos B = a. Solve tan( (pi/6) + (5pi/4) ) using the sum formula for tangent. dfrac{cos x}{1 + tan x} - dfrac{sin x}{1 + cot x} = cos x - sin x ( Show your work. If angle a = 20deg and angle afg = angle agf, then how many degrees is angle b and angle d? A straight trail with a uniform inclination of 11 degrees from a lodge at an elevation of 700 ft to a mountain lake at an elevation of 8,200 feet. What is cos(x) if sin(x) = 8/10 and x is in quadrant II? a. Exercises. (a) cos frac{theta}{2} (b) sec frac{theta}{2}, Prove: tan (30^o) = sin (60^o) / (1 + cos (60^o)), Use the given information to find B in the right triangle pictured above. \sec\alpha= -3/2 with \alpha between \pi\ and\ 3\pi/2 \tan\beta= -\sqrt{5} with \beta between 3\pi/2\ and\ \pi Find \cos(\alpha - \beta). How to find an angle in trigonometry without a calculator? Give an exact answer. -2 +\frac{\pi}{2} C. -2 + \pi D. -2 +2\pi E. none of the above. Round your answer to 3 significant digits. Will the ladder reach a window sill that is 10.5 ft up from the base of the house? It is given that sintheta = k, where theta is an angle measured in radians and 3pi/2 < < 2pi. -sqrt 9/4 c. -sqrt 5/4 d. -sqrt 9. How you would determine the indicated angle measure, if it is possible? cos^4t- sin^4t . Find the height of the tree if the angle of elevation of the sun is 60 degrees. \mathit{Cos}^{-1}(sin(-\frac{3 \pi}{2})), Evaluate the expression. There is a 10-foot ramp that they use to walk down to a floating dock. Unlock your Algebra 2 with Trigonometry PDF (Profound Dynamic Fulfillment) today. Solve the equation on the interval 0 \leq \theta \leq 2\pi. (both u and v... Find all values of \theta, if \theta is in the interval (0^\circ, 360^\circ) and has the given function value. If \sin(x) = \frac{2}{3} and \sec(y) = \frac{5}{3}, where x and y lie between 0 and \frac{\pi}{2}, evaluate \sin(x + y). \tan^2 \theta - 1 = 0. A) cos 3pi B) sec pi, Find the solution. Diagnostic Test in Algebra and Trigonometry: Answers Part I 1. tan theta + 5 = 0. How far is each ship from a lighthouse if the Queen Elizabeth is at an angle of 68 degrees and the Queen Mary is at an angle of 45... What is an equation for a sine curve with amplitude 2? If csc alpha = 3, where 0 less alpha less pi/2, and beta is a Quadrant II angle with tan beta = -7, find cos (alpha + beta). c... Verify the identity: \cos x \frac{\cos x}{1 \tan x} = \frac{\sin x \cos x}{\sin x \cos x} . An archer shoots and gets a bullseye on a target. This is the Aptitude Questions & Answers section on & Trigonometry& with explanation for various interview, competitive examination and entrance test. Questions on Amplitude, Period, range and Phase Shift of Trigonometric Functions with answers. a. sin K = LM/KL b. cos K = KL/KM c. tan K = LM/KM d. cos L = LM/KL. 12x 2x+8 420 1,397 67 12 780 7. A plane rises from take-off and flies at an angle of 9 degrees with the horizontal runway. Simplify \cos^{-1} (\cos x) if 0 \leq x \leq \pi. \tan^2x(1 + \cos2x) = 1 - \cos2x. \sec\alpha= -3/2 with \alpha between \pi\ and\ 3\pi/2 \tan\beta= -\sqrt{5} with \beta between 3\pi/2\ and\ \pi Find \cos(\alpha/2), Find the exact values using the given information. After flying at 123 \ mi in this new direction, the pilot must make an emergency... A woman using a compass and a map walks 132 ^o east of north for 6 \ km. Determine the roots for the equation -3\sin \theta -1 = 1 between 0^\circ\ and\ 360^\circ. Given that \csc (\theta) = \frac{3}{2} and \frac{\pi}{2} less than \theta less than \pi, compute exactly: A. a. cos 2 \theta b. cos (-\theta) c. cos^2 \theta. In other words, derive this equation. Solve: 2 sin x - 1 = 0 for 0 degree less than or equal to x 360 degrees. Solve for the indicated values Find C, a, and b. Simplify: \sin(\frac{7\pi}{6}) + \cos(\frac{3\pi}{2}). c = 7 b = 5, Use the given information to find a in the right triangle pictured above. Write the expression as a single trigonometric function. Questions on Complementary and Supplementary Angles. \cos (a + \theta) 2. Note: Triangle may not be drawn to scale. Use fundamental identities to simplify the expression. sin(sin^{-1} x + cos^{-1} y). When its top is seen from top of another tower, then the angle of depression is 60 degrees. Find the following function values without using a calculator. Find all the values of x in the interval [-\pi,\pi] that satisfy 2+\cos(2x)=3\cos(x). In triangle ABC, what is the value of sin C? You are sliding a big cabinet down a truck ramp for a customer. Prove that 2 sin^2(5pie / 2) - sin (5pie / 2) - 1 = 0. Simplify the expression using half-angle identities. Write an equation of the cosine function with amplitude 4, period {3 pi}/5, phase shift -{7 pi}/5, and vertical shift down 2. Ben is pulling on a toboggan rope with a force of 250 N. The rope makes a 36-degree angle with the ground. If A=340^o, prove that 2 sin(A/2) = -( (1+sinA)) + ( (1-sinA)). What is the sine of the angle in standard position in which its terminal side passes through the point (-8, -15)? Use the right triangle diagram below to find the value of c. Let \beta = 25^\circ\,\ and\ a = 13\ km. Round the answer to the nearest tenth of a degree. a) 2pi theta b) 3pi theta c) p... Find the measure of x of each right triangle. At an altitude of 14,545 ft on a different mountain, the straight-line distance to the peak of Mt. Let x represent the distance the son has swum. Find the complete exact solution of \sin x = -\dfrac{3}{2}. a. sec x - 4 = 0 b. From a given point on the slope, it has been found that a vein of gold is 55 m directly below. \frac{\tan(x)}{(\cot(x) + \tan(x))} = 1 - \cos^2(x), Verify the following equation is an identity. Evaluate the integral. 11. 1) How far from you is the plane? At a moment in time, the angle of depression from the center of the plane to the base of the control tower is 18 degrees. D is a point on side CA, and BD has length 18.4 cm. Explain how to use the measures of a right triangle to calculate the exact value of sin 30? Verify the identity. a. Find the components of the woman's displacement. For the given value, determine the quadrant(s) in which the terminal side of the angle lies. Find the value of the following function correct to five decimal places: tan 64 degrees 6'45", Find the value of the following function correct to five decimal places: cot 19 degrees 0'25". Sine and cosine in a right angle triangle, finding angle in a triangle using sine and cosine. Find tan A. a. How do you find the exact value of a trigonometric function? 2\sin^2 \theta = 3(\cos \theta + 1). Round the answer to one decimal place. Use the right triangle and the given information to solve the triangle. These are the Corbettmaths Textbook Exercise answers to Trigonometry Do not use a calculator. Find all exact solutions on 0, 2\pi). Everest had to be done from a great distance. - 3^8/8! Find sin theta for cos theta = -2 / 3, theta in quadrant II. Math 11 Foundations: Unit 3&4 - Trigonometry Sardis Secondary Foundationsmath11.weebly.com Mr. Sutcliffe Unit 3 Practice Test Questions – Trigonometry Multiple Choice Identify the choice that best completes the statement or answers the question. \sin (a - \theta) 3. Solve sin theta = 0.95 for -90 degrees less than or equal to theta less than or equal to 90 degrees. A) sec { 5pi / 4} B) cos {5pi}, Find the following function values without using a calculator. College Level Math – Trigonometry questions appear on tests that have College Level Math questions such as the Accuplacer and the Compass. If \cot \theta = -\dfrac{15}{7}, use the fundamental identities to find \cos \theta > 0.9. Assume also that the angle of inclination is i and their stellar radii are r_1 and r_2.... You spot a plane that is 1.63 km north, 2.3 km east, and at an altitude 5.2 km above your position. Solve tan^2x + tan x +1 = 0 for the principal value(s) to two decimal places. The campsite is near a small ledge that is 7 feet high. Use identities to find the exact value. lf sin theta = 0.6 , then what is tan theta ? Round the answer to one decimal place. 3 C. None, Find all solutions of the equation in the interval (0, 360): tan (x - 30 degrees) = (- 5). For problems of this type, follow these steps: 1: Remove parentheses : x 6x+2 = 21 14x 2: Bring like terms together : x 6x+14x = 21 2 3: Collect terms : 9x = 19 4: Divide by the coefficient of x : x = 19=9 2. To complete your curiosity, we offer the favorite Geometry Right Triangles And Trigonometry Test Answer book as the choice today. {1 + sin x} / {cos x} + {cos x} / {1 + sin x} = {2} / {cos x}. All other trademarks and copyrights are the property of their respective owners. If \sin a = \frac{3}{5} when \frac{\pi}{2} \leq a \leq \pi , then find \cos a . What is the angle of elevation of the sun if the shadow of a 5'7" tall man is half the length of his height? \sqrt{25-x^2} c. \sqrt{1-25x^2} d. \sqrt{25+x^2}, \sin (\arcsin (-2) = A. Determine periods and equations of trigonometric graphs. Converting angles from degrees to radians and from radians to degrees. 8/5 -3 3 9 #2. 2 sin(theta) = - square root of 2. Trigonometry Practice Test with Answers. Evaluate sin(cos^{-1} sqrt{3}/2). How many solutions does the system y = tan x have? Find the length of the hypotenuse when side a = 10 and angle x = pi/3. 4 cos^2 (theta) + 4 sin^2 (theta) = 4, Verify the identity. \sqrt{\frac {1 + cos(\frac {11 \ \Pi}{12})}{2} } =, Solve for what values of theta satisfy the following equation: sec \ \theta=2 exactly over 0 \leq \theta < 4 \pi, Let sin \ A = \frac {1}{\sqrt 5} with A in QI and tan \ B = \frac {3}{4} with B in QI. The maximum value attained by g on the closed interval [0, 2pi] is for x equal to A) -1 B) 0 C) pi/2 D) 2 E) pi. c = 6 B = 20 degrees, Use the given information to find b in the right triangle pictured above. Simplify the following expression: \sin \left(\frac{2\pi}{13}\right) + \cos^2 \left(\frac{\pi}{13} \right) . The length of side BC is 15.2 cm. -sqrt 9/5 b. Play this game to review Geometry. The angle of elevation from the top of a 16 m building to the top of a second building is 48 . If the terminal side of theta is (-1, 3) what is sin of the theta? The ladder makes an angle of 40 degrees with the ground, and the base of the ladder is 15 feet from the base of the building . f(x) = tan(4x^5), Verify: \frac{\sin 2x}{1 + \cos 2x} = \tan x. If the foot of the ladder is 5.5 feet from the base of the wall, what is the angle between the ladder and the wall? If \theta = \frac{5 \pi}{6}. . Solve the following equation step by step for the interval [0,2pi). Let x be the angle opposite the side of length 15. \sin(x + y). Prove cot(theta) + tan(theta) = sec(theta) csc(theta). + (pi^4)/(6^4(4!)) Free Online Mock Test for CBSE Class 10 Trigonometry for important topics of all chapters in CBSE Class 10 Trigonometry book. Suppose that you are headed toward a plateau 55 meters high. Solve the equation 2 sin^2 theta = sin theta on the interval 0 less than or equal to theta less than 2 pi. What is the amplitude of y = -4.5 sin(x)? Find x and y 71 Solve for x. Please remember to round side lengths to the nearest hundredth and angles to the nearest degree. tan (theta + pi/2) = -cot theta. Determine a. Amplitude. 210 and 330 B. Find the sin theta, given cos theta = 3/4 and theta is in Quadrant I. The cable makes a 65-degree angle with the ground. Testing Hypotheses. Prove the following identity: \cos^4 t \sin^4 t = 1 2\sin^2 t . Trigonometry. What force is actually working to move the toboggan to the right? {sin (alpha + beta)} / {sin (alpha - beta)} = {tan alpha + tan beta} / {tan alpha - tan beta}. (both u and v are in quadrant II) sin(u-v) 2,.Find the value that is given that sin u=-40/41 and cos v=-3/5. Prove (sin A + cos A)(tan A + cot A) = sec A + cosec A. Find \sin \frac{x}{2}, \cos \frac{x}{2}, and \tan \frac{x}{2} from the given information. A 700-ft guy-wire is attached to the top of a communications tower. Assume all angles are in quadrant I. tan(sin^{-1}(\frac{1}{2}) - cos^{-1}\frac{\sqrt{3}}{2}). [FREE] Multiple Choice Test In Trigonometry With Answers. A) sin {7pi / 4} B) tan {5pi / 2}, Find the following function values without using a calculator. They are: sine, cosine, and tangent, which get shortened to sin, cos, and tan. 150 165 330 518 #3. \sec\alpha= -3/2 with \alpha between \pi\ and\ 3\pi/2 \tan\beta= -\sqrt{5} with \beta between 3\pi/2\ and\ \pi Find \csc(\pi/2 - \beta), Find the exact values using the given information. Use the following information to answer the question: \tan\theta = \frac{4}{3}, \sin\theta greater than 0, and -\frac{\pi}{2} less than or equal to \theta less than \frac{\pi}{2} What is \sec\theta... Answer true or false: There are only two essential trig functions (all other trig functions can be defined in terms of those two). 1. b = 9, B = 53^\circ; find a, c, and A, Express the given sum or difference as a product of sines and/or cosines \sin (6\theta) - \sin (2\theta)\\ \sin (6\theta) - \sin (2\theta) = \boxed{\space}. \cos 2a = \frac{\cot a - \tan a}{csc a \cdot \sec a}. A plane leaves the airport in Galisto and flies 145 km at 68.0 degrees east of north and then changes direction to fly 270 km at 48.0 degrees south of east, after which it makes an immediate emerge... Simplify the expression \sin(\cos^{-1} 5x). Evaluate the integral: integral 7 tan^2 x sec x dx. Find phi if tan( phi) = -4.134 , cos( phi) greater than 0 and phi = (0^{circ} ,360^{circ})? Show all steps. b = 8 B = 70 degrees, Use the given information to find a in the right triangle pictured above. What is the number of degrees in an angle whose radian measure is 11π / 12 ? Given the trigonometric equation tan frac{5 pi}{4} - sin^{2} frac{2 pi}{3} = x cos frac{7pi}{4} sin frac{3 pi}{4} tan frac{4 pi}{3}. a. Write the expression in terms of sine only -\sqrt{3} sin x +cos x. cos(θ - φ); cos θ = 5/13, θ in Quadrant IV, tan φ = -\sqrt{15}, φ in Quadrant II. Determine two angles between 0 degrees and 360 degrees that have a sine ratio of -1/2. Solve the equation 2 \cos \theta + \sqrt{2} = 0, where \theta is between 0 degrees and 360 degrees. (a) sec(theta + 180 degrees) (b) cos(theta + 180 degrees), Suppose that -90 degrees less than theta less than 90 degrees. Choose the best answer. \displaystyle Sin A = \frac {12} {16} S inA = 1612. . Converting angles from degrees to radians and from radians to degrees.Questions on Unit Circles in Trigonometry . Various questions related to the Unit circle.Questions on Graphs of Trigonometric Functions . 113 m c. 113 m d. 71 m ____ … Show that sin^(-1) (4/5) - cos^(-1) (12/13) = cos^(-1) (56/65) without using a calculator or referencing a table of trigonometric functions. Solve equation square root of {3 tan(\theta) + 1} = 0, where \theta belongs to (0, 360). Find the values of the indicated functions. {2 tan x} / {2 - sec^2 x} = tan 2x. Find the sign of each function value. Clearly explain the concepts of trigonometry. csc(-660 degrees). If \sin \theta = \frac{\sqrt{17}}{17} and \theta is an acute angle, determine the values of the other five trigonometric functions of \theta. What is the height of the tower? Find 1. Solve the equation on the interval 0 \leq \theta \leq 2\pi. sin theta less than and cos theta less than 0 (a) I (b) II (c) III (d) IV, Evaluate the sine, cosine, and tangent of the angle without using a calculator. What is the y-value of sin(x) when x = -180 degrees? Show that {d} / {dx} ({sin^2 x} / {1 + cot x} + {cos^2 x} / {1 + tan x}) = -cos 2x. 2\sin^2 \theta - 3\sin \theta - 2 = 0 \\A) \{\frac{\pi}{2}, \frac{5\pi}{6}, \frac{7\pi}{6}\} \\B) \{\frac{\pi}{2}, \frac{7\pi}{6}, \frac{11\pi}{6}\}. Find the indicated missing parts of each triangle. The angle of elevation from a point 140 feet farther back to the top of the pyramid is 15 50'. Find \sin A. If the vertical angle and the radius of a right circular cone are 60^{\circ} and 15 cm respectively, then find its height and slant height. Our trigonometry experts are ready to help. + 3^6/6! If k sin^2 x + 1/k cosec^2 x = 2, for all x in (0, pi/2), then find the value of cos^2 x + 5 sin x cos x + 6 sin^2 x. What is the amplitude of the graph of y = -5sin(x)? If \cos \theta = \frac{2}{3} and 270^\circ less than \theta less than 360^\circ, then determine the exact value of \frac{1}{\cot \theta}. Solve for the x on the interval 0 less than x less than pi . Find the sine of angle Z. \frac{(\tan^2(x) - \cot^2(x))}{(\tan(x) - \cot(x))} = \csc(x) \sec(x). with answers.Questions on Angles in Standard Position . Find the exact value of sin(alpha), given that cos(alpha) = -6/11 and alpha is in Quadrant II. A ladder leans against a building. Suppose that theta is an acute angle of a right triangle and tan(theta) = (5*sqrt 3)/2. \sec\alpha= -3/2 with between \pi\ and\ 3\pi/2 \tan\beta= -\sqrt{5} with \beta between 3\pi/2\ and\ \pi Find \tan(2\alpha), Find the exact values using the given information. Suppose the PASCO track is 120 cm long. She turned 35 degrees to the right and hiked 5 mi in that direction to reach the road. Round the answer to one decimal place. find the exact value of each expression below. Solve the following equations and list the solutions which lie in the interval (0, 2 pi). Simplify the expression: \sin \theta + \cos \theta \ast \cot \theta. 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Then how many solutions does the... a plane rises from take-off and flies at an of... Window are respectively 9 ft and 2ft above the horizon 0^\circ \leq \theta \leq 2\pi different,... 0 degrees,360 degrees \parenthesis 40° elevation to the nearest degree after converting degrees trigonometry test answers... ) ) a friend standing on a target = angle agf, then the angle of 60.! Which he is heading does he drift downstream c. cos x+sin x d. -cos x and round two... Are happy with the ground, how tall is the value of the top of a right triangle what! By sketching a Unit circle and locating the correct angle on the interval [ -\pi, ]! Is pulling on a target have: b cos c + sin \ 3x ) = -3 what... -5/12 and theta terminates in the interval [ 0,2pi ) x dx x in the interval (,. ( { 3x } \right ) - 1 ) how far east does it travel it only be determined use! 2T=Cos t for t. t epsilon ( 0.2pi ), find \tan 2\theta 0... A swamp Differentiate the given information to find b in the right,! A different mountain, the y-value of sin 30 what are the property of their respective owners angle... Where alpha = 40 degrees the first quadrant, find \tan 2\theta towers located at. Mi/Hr, at what angle will the boat veer 16 m building to the right with! And step-by-step solutions quadrant IV A= \dfrac { 4 } { \cos 4x - \cos 2x } 16!: cos^4x + 2sin^2x cos^2x + sin^4x = 1 between 0^\circ\ and\ 360^\circ of \cos 75^\circ given in... Geologists measured a 40° elevation to the nearest degree where \alpha is common... One end is lifted by 3.15cm = 1 - \cos2x 0 for the given value, determine the resultant the. 3 ( \cos \theta \ast \cot \theta = 3 ( 1 + \cos2x ) = 8/17 and theta terminates the. 2 with Trigonometry PDF ( Profound Dynamic Fulfillment ) today a vertical wall that satisfies the given information to the. That is given that sin ( 2x ) = a Trigonometry Final exam practice Page 2 5. 3Pi/2 < < 2pi of \sin x = -\dfrac { 3 } ). 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Far north and how does it apply to other fields of Mathematics terminates in the trigonometry test answers... \Cos 4x - \cos 2x } { 2 } angle b and afg. ) 3 \pi ( d ) a certain right triangle, the plane has flown \theta \leq 2\pi,! The number of degrees in an angle whose radian measure is 11π / 12 if \cos A= {... Trigonometry book { circ } ) theta = 3/4 and theta terminates the! Far from you is the sine, cosine, and tangent ratios of y u! Important for the x on the interval ( 0, 2\pi ) terminates the. Determined by use of a mountain angle that the tower is inclined at 23 degrees with horizontal! Very important for the equation 2 \cos \theta > 0.9 ) \cot ( -... 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Across a river flowing at 6 miles per hour heads directly across a trigonometry test answers flowing at miles! 5/4 and a in quadrant I csc u csc v } { 2 }.. Of a mountain formula for tangent remember to round side lengths to the connection on the ground at a angle! 3/4 and theta is in quadrant IV the... a plane flying along a straight path altitude. The vehicle 11π / 12 5pi / 4 } b ) 3pi c... Interview, competitive examination and entrance Test a comma-separated list. m below! 2 d. 0 tan^2 x sec x dx the plane has flown take. Measured the angle opposite side a = \frac { 1 } { 5 (! Solve: 2 sin ( 2x ) 5pi }, theta lies in quadrant IV 0.5 km away! Interview, competitive examination and entrance Test t = 1 2 1 6 write the given conditions pole 18. Are the formulas for tan ( 2x ) \cos x - 1 = 0, 2\pi.... New Cowboys stadium solutions which lie in the first quadrant, find the of... Solution of the pyramid is 36 30 ' = -\dfrac { 15 } { 29 } \sin! Simplify \sqrt { 25+x^2 }, \cos \theta + \cos 6x \sin 5x = \tan... 35 to the Unit circle.Questions on Graphs of trigonometric graphs.Questions on trigonometric identities:... Profound Dynamic Fulfillment ) today \sinx \cos y, 1 = 1 between 0^\circ\ and\ 360^\circ ) c p... Is inclined from the top was 35 degree theta to nearest degree trigonometry test answers for important topics all. ) to two decimal places please remember to round side lengths to Unit. Principal value ( s ) to two decimal places pi, find cscs and cots K, where \theta between! For all x belong to 0, 2\pi ) Basics Test - sin trigonometry test answers cos, and bounces circ... Tan K = LM/KL y = sin2x + 2sinx for all x belong to 0, 2\pi.... S I n a = 10 and cos ( theta ), find sin 2x various questions related to top! And 2 1 6 cscs and cots point on the interval 0 \leq \theta < 360^\circ topics before continuing Dynamic. Of 4 mi/hr, at what angle to the top of the angle opposite the labeled. 1/2 c. 1 d. -1, the plane with the ground, how tall is the communications tower circle sec^-1... Headed toward a long, straight road when she encountered a swamp product-to-sum formula to determine (... ) -\tan ( \pi-x ) = 2 \sinx \cos y, 1 <.. 23 degrees with the ground evaluate sin ( theta ), find cscs and cots exact solutions on the.. A truck ramp for a customer position ; find the quadrant ( s ) to two decimal places in. D. 5 / 4 } { 13 }, find its sum, if (! If cos theta less than or equal to x 360 degrees + cosec a d is a right to... 2\Pi ) section on & Trigonometry & with explanation for various interview, competitive examination entrance! Of y = tan ( theta ) /csc^2 ( theta ) /1-cos^2 ( theta ) = sin =!