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
3x = sin x ( - 1 + 4 cos2x )
sin(4x) = cos x ( 4 sin x - 8 sin
3x ) = sin x ( - 4 cos x + 8 cos3x )
sin(5x) = 5 sin x -20 sin
3x + 16 sin5x = sin x ( 1 - 12 cos2x + 16 cos4x )
cos(2x) = cos
2x - sin2x = - 1 + 2 cos2x
cos(3x) = cos
3x - 3 cos x sin2x = -3 cos x + 4 cos3x
cos(4x) = cos
4x - 6 cos2x sin2x +sin4x = 1 - 8 cos2x + 8 cos4x
cos(5x) = cos
5x - 10 cos3x sin2x + 5 cos x sin4x = 5 cos x - 20 cos3x + 16 cos5x
tan(2x) = 2 tan x / (1 - tan
2x)
tan(3x) = ( 3 tan x - tan
3x ) / (1 - 3 tan2x)
tan(4x) = ( 4 tan x - 4 tan
3x ) / (1 - 6 tan2x + tan4x)

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

  1. c)
  2. a)
  3. b)
  4. b)
  5. d)
  6. c)

Links and References

Trigonometry Problems