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)
  1. Question 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


  2. Question If cos t = 0.8, then cos (2 t) = ?

    a) 0.28
    b) 0.4
    c) 1.0
    d) 1.6


  3. Question If tan x = 5, then tan (2 x) = ?

    a) 10
    b) - 5 / 12
    c) 1 / 10
    d) 5 / 12


  4. Question 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


  5. Question If cos t = 1/3 and 3 π /2 < t < 2 π in quadrant IV, then sin (4 t) = ?

    a) 8 √2 / 3
    b) - 8 √2 / 3
    c) - 56 √2 / 243
    d) 56 √2 / 81


  6. Question 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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