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 Functions
sin(2x) = 2 sin x cos xsin(3x) = 3 sin x - 4 sin 3 x = sin x ( - 1 + 4 cos 2 x )
sin(4x) = cos x ( 4 sin x - 8 sin 3 x ) = sin x ( - 4 cos x + 8 cos 3 x )
sin(5x) = 5 sin x -20 sin 3 x + 16 sin 5 x = sin x ( 1 - 12 cos 2 x + 16 cos 4 x )
cos(2x) = cos 2 x - sin 2 x = - 1 + 2 cos 2 x
cos(3x) = cos 3 x - 3 cos x sin 2 x = -3 cos x + 4 cos 3 x
cos(4x) = cos 4 x - 6 cos 2 x sin 2 x +sin 4 x = 1 - 8 cos 2 x + 8 cos 4 x
cos(5x) = cos 5 x - 10 cos 3 x sin 2 x + 5 cos x sin 4 x = 5 cos x - 20 cos 3 x + 16 cos 5 x
tan(2x) = 2 tan x / (1 - tan 2 x)
tan(3x) = ( 3 tan x - tan 3 x ) / (1 - 3 tan 2 x)
tan(4x) = ( 4 tan x - 4 tan 3 x ) / (1 - 6 tan 2 x + tan 4 x)
Questions with their Answers
Question 1
If 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 2
If cos t = 0.8, then cos (2 t) = ?a) 0.28
b) 0.4
c) 1.0
d) 1.6
Question 3
If tan x = 5, then tan (2 x) = ?a) 10
b) - 5 / 12
c) 1 / 10
d) 5 / 12
Question 4
If 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 5
If 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 6
If 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
Answers
- c)
- a)
- b)
- b)
- d)
- c)
