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)

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)

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