Questions on Trigonometric Functions of Multiple Angles
Multiple choice questions on evaluating trigonometric functions of multiple angles with answers at the bottom of the page. Formulas of Multiple Angles in Trigonometric Functionssin(2x) = 2 sin x cos xsin(3x) = 3 sin x - 4 sin3x = sin x ( - 1 + 4 cos2x ) sin(4x) = cos x ( 4 sin x - 8 sin3x ) = sin x ( - 4 cos x + 8 cos3x ) sin(5x) = 5 sin x -20 sin3x + 16 sin5x = sin x ( 1 - 12 cos2x + 16 cos4x ) cos(2x) = cos2x - sin2x = - 1 + 2 cos2x cos(3x) = cos3x - 3 cos x sin2x = -3 cos x + 4 cos3x cos(4x) = cos4x - 6 cos2x sin2x +sin4x = 1 - 8 cos2x + 8 cos4x cos(5x) = cos5x - 10 cos3x sin2x + 5 cos x sin4x = 5 cos x - 20 cos3x + 16 cos5x tan(2x) = 2 tan x / (1 - tan2x) tan(3x) = ( 3 tan x - tan3x ) / (1 - 3 tan2x) tan(4x) = ( 4 tan x - 4 tan3x ) / (1 - 6 tan2x + tan4x) QuestionsQuestion 1If sin t = 0.6 and cot t > 0, then sin (2 t) = ?a) - 0.96 b) 0.48 c) 0.96 d) - 0.48 Question 2If cos t = 0.8, then cos (2 t) = ?a) 0.28 b) 0.4 c) 1.0 d) 1.6 Question 3If tan x = 5, then tan (2 x) = ?a) 10 b) - 5 / 12 c) 1 / 10 d) 5 / 12 Question 4If cos t = 3/4, and sin t < 0, then sin (3 t) = ?a) √7 / 16 b) - 5 √7 / 16 c) - 3 √7 / 4 d) 5 √7 / 16 Question 5If cos t = 1/3 and 3π /2 < t < 2π in quadrant IV, then sin (4 t) = ?a) 8 √2 / 3 b) - 8 √2 / 3 c) - 56 √2 / 243 d) 56 √2 / 81 Question 6If sin t = 1/5 and 0 < t < π/ 2, then cos (4 t) = ?a) 0.3464 b) 0.8 c) 0.6928 d) - 0.6928 More |
