a) sin(7π)/(4) b) sec(2π)/(3) c) cot(11π)/(6) d) cos(3π)/(4) Find all values for 0<=θ<=2π. a) cosθ = (√3)/(2) b) secθ = -√2 c) cotθ = -1 d) tanθ = √3 Solve: a) sin2θ = (1)/(2) b) cos((θ)/(2)) = -(1)/(2) c) cos(θ + (π)/(3)) = (1)/(2) Solve: a) cos^2x = (3)/(4) b) 2sin^2x + sinx - 1 = 0 c) 10cos^2(2x) + 7cos(2x) = 6 d) 4cos^2(2x) - 1 = 0 e) 2tan^2x + tanx - 3 = 0 f) 6cos^2x - sinx - 4 = 0 g) 2cosx = 1 - sin^2x Evaluate the following: a) cos((5π)/(6)) b) sec((11π)/(3)) c) sin(π)/(12) d) tan(11π)/(12) Write as a single trig function. a) sinAcosB - cosAsinB b) (2tanx)/(1 - tan^2x) c) 10sinxcosx d) 1 - 2sin^2((2θ)/(3)) e) -4sin(x)/(2)cos(x)/(2) f) (tan3x - tan4x)/(1 - tan3xtan4x)
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Step 1: a) sin(7π)/(4) Using the unit circle, we know that sin(7π)/(4) = sin(π/4) = √2/2 Show more…
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Ankit S.
Find the exact value of each of the remaining trigonometric functions of θ. Rationalize denominators when applicable. sec θ = -11, given that sin θ > 0 sin θ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) The function is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. cos θ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) The function is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. tan θ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) The function is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. csc θ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) The function is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. cot θ =
Supreeta N.
TUTORIAL 6 TRYGONOMETRY 1. Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. a. 75° c. -61° b. 174° d. -90° 2. Sketch an angle (θ) in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the three trigonometric functions for each angle. Rationalize denominators when applicable. a. (5, -12) c. (-8, 15) b. (3, 4) d. (-7, -24) 3. Find the exact value of a. cos(tan⁻¹ 5/12) b. cot(sin⁻¹ -1/3) 4. Solve for x: a. π + 3cos⁻¹(x + 1) = 0 b. 2tan⁻¹(1/2) = cos⁻¹x c. sin⁻¹ x = cos⁻¹(2x) 5. Proof a. tan x + cos x = sin x (sec x + cot x) b. 2cos⁻¹(4/5) = cos⁻¹(7/25) c. 1 + cos θ = sin²θ / (1 - cosθ) d. tan x + cot x = sec x csc x e. sin(2tan⁻¹x) = 2x / (x² + 1)
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