Rewrite the expression as a sum or difference: - 2(sin \ 7x + sin \ 3x) . . Top 15 RRB NTPC Maths questions based on asked questions in previous exam papers very important for the Railway NTPC exam. Go ahead and ask it. Solve sin theta = 0.95 for -90 degrees less than or equal to theta less than or equal to 90 degrees. If a boat going 6 mi/hr in still water suddenly encounters a crosscurrent of 4 mi/hr, at what angle will the boat veer? Establish the following identities: sec^4 theta - tan^4 theta = dfrac{1 + sin^2 theta}{ 1 - sin^2 theta }, Verify identity. How much should a ramp rise over 10 meters of run for an angle of 12 degrees? Solve, finding all exact solutions, in radians, in the interval \parenthesis 0,2\pi). Given a right triangle having an acute angle of 14 degrees and a hypotenuse of length 50, find the measurement of the other angle and the measurements of the other sides. After moving 0.5 km farther away, the angle of elevation was 34°. One member of the group has an altimeter on his watch to measure altitude. c = 6 B = 20 degrees, Use the given information to find b in the right triangle pictured above. When he walked 30 m further away, the angle of elevation of the top was 35 degree. - 3^4/4! If csc alpha = 3, where 0 less alpha less pi/2, and beta is a Quadrant II angle with tan beta = -7, find tan (alpha + beta). Given cos (theta) = 1/5 what is sin (theta)? Leave your answer in simplest radical form. Find tan A. a. -sqrt 9/5 b. . . (1) -pie / 3 (2) 2 pie / 3 (3) 5 pie / 6 (4) 120 degrees. lf sin theta = 0.6 , then what is tan theta ? Find the exact value. (sin 82.5^{circ})(cos 37.5^{circ}). -2 +\frac{\pi}{2} C. -2 + \pi D. -2 +2\pi E. none of the above. 2 / 5 C. 5 / 2 D. 5 / 4, Using the following triangle, what is the cosine of angle B? a. sec x - 4 = 0 b. If A=340^o, prove that 2 sin(A/2) = -( (1+sinA)) + ( (1-sinA)). tan theta = 1.700. \frac{\tan(x)}{(\cot(x) + \tan(x))} = 1 - \cos^2(x), Verify the following equation is an identity. What is the sine of the angle in standard position in which its terminal side passes through the point (-8, -15)? {pi/2, 3 pi/2, pi / 3, 2 pi/3} c. {0, pi, pi/6, 5 pi/6} d. {pi/6, 5... Find the exact value of the expression sin (pi/3) - cos (pi/6). Round the answer to one decimal place. Find \sin(\alpha) , where \alpha is the angle opposite side a . Solve: 2 sin x - 1 = 0 for 0 degree less than or equal to x 360 degrees. Trigonometry Questions and Answers Test your understanding with practice problems and step-by-step solutions. The angle of elevation from a point on the ground to the top of a pyramid is 36 30'. Find the following function values without using a calculator. Choose the best answer. Solve: x 2(3x 1) = 7(3 2x). 1) How far from you is the plane? {1} / {1 - csc theta} - {1} / {1 + csc theta} = -2 tan theta sec theta. c = 2 B = 9 degrees, Use the given information to find c in the right triangle pictured above. A ball is launched from the ground at a 45-degree angle above the horizontal (which we take to be the x-axis). Find x. Exercises. If the angle of elevation to the top of the plateau is 40 degrees, how far are you from the base of the plateau? What is the height of the telephone pole to the near... Verify the identity. \csc (2 \theta) C. \tan (2 \theta), Solve identity \frac{1 - \sin 2x}{\cos 2x} = \frac{\cos 2x}{1 + \sin 2x}. Verify the expression: cos^4x + 2sin^2x cos^2x + sin^4x = 1. Find the value of \tan (a b) if \cos a = \frac{3}{5} \text{ and } \sin b = \frac{5}{13} . Find the exact value of x that satisfies the given conditions. c... Verify the identity: \cos x \frac{\cos x}{1 \tan x} = \frac{\sin x \cos x}{\sin x \cos x} . Show that following trigonometric functions are bounded. Given the figure below, suppose a = 11 and b = 6. A. Infinitely many B. After the bo... KLM is a right triangle with a right angle at M. Which of the given statements is false? \sqrt{25-x^2} c. \sqrt{1-25x^2} d. \sqrt{25+x^2}, \sin (\arcsin (-2) = A. \cos^2 \theta = 3(1 -\sin \theta). Given that theta is an angle between pi and 3 pi / 2 , such that cot theta = 3/5 . 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. cot^2(4x) tan(2x) - tan(2x) = 0. Find exact values for: a. sin theta b. tan(2 theta) c. sin( pi/2 - theta). True B. \sin (a - \theta) 3. Suppose T q42 is a central angle in a circle with radius of 14.2 meters. Services, Working Scholars® Bringing Tuition-Free College to the Community. Round the answer to the nearest tenth of a degree. A person attempts to measure the height of a building by walking out a distance of 35.0 m from its base and shining a flashlight beam toward its top. Solutions to the Above Problems. In triangle GHI, we have GH = HI = 25 and GI = 40. 1-cos (theta)/sin (theta) = csc (theta) - cot (theta), Suppose theta is a Quadrant I angle with tan theta = x. Verify the formula: cos (2 theta) = 1 - x2 / x2 + 1, Suppose theta is a Quadrant I angle with tan theta = x. Verify the formula: sin (2 theta) = 2x/ x2 + 1, Suppose theta is Quadrant I angle with sin theta = x. Verify the formula: cos theta = sqrt(1 - x2). 4 3 cos 13. Simplify the following expression: \sin \left(\frac{2\pi}{13}\right) + \cos^2 \left(\frac{\pi}{13} \right) . This carefully selected compilation of exam questions has fully-worked solutions designed for students to go through at home, ... GCSE 9-1 Exam Question Practice (Trigonometry) 5 79 customer reviews. 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Complementary and Supplementary angles.Questions on converting angles from degrees to radians and