Questions on Solving Simple Trigonometric Equations

Multiple choice questions on solving simple trigonometric equations with answers at the bottom of the page.

  1. Question If 0 < t < 2π such that sin t = √2 / 2 and cot t < 0, then t = ?

    a) π / 4
    b) 5 π / 4
    c) 7 π / 4
    d) 3 π / 4


  2. Question If 0 < t < 2π and sin t = - 1, then t =

    a) π / 2
    b) 3 π / 2
    c) 5 π / 4
    d) π


  3. Question If - 2π < t < 0 and sin t = - 1 / 2, then t =

    a) -5 π / 6
    b) -7 π / 6
    c) - 5 π / 4
    d) - 5 π / 3


  4. Question If 0 < α < π and cos α = -√3 / 2, then α =

    a) π / 6
    b) - π / 6
    c) 7 π / 6
    d) 5 π / 6


  5. Question Find all values of t such that sin(t) = 0.

    a) t = kπ/2 ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...
    b) t = kπ/4 ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...
    c) t = kπ ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...
    d) t = 2 kπ ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...


  6. Question Find all values of t such that cos(π t) = 1.

    a) t = 2 k π ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...
    b) t = 2 k ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...
    c) t = k ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...
    d) t = k π ; k = 0, ~+mn~ 1, ~+mn~ 2, ~+mn~ 3,...


  7. Question Find all angles θ such that -2π < θ < 2π and cos θ = √2 / 2

    a) {-7 π / 4, - π / 4 , π / 4 , 7 π / 4}
    b) {- π / 4, - 3 π / 4 , π / 4 , 3 π / 4}
    c) {-5 π / 4, π / 4 , 3 π / 4}
    d) {π / 4 , π / 4 , 3 π / 4}


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

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