# 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 x
sin(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)

### 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