Questions on Solving Simple Trigonometric Equations
Multiple choice questions on solving simple trigonometric equations with answers at the bottom of the page.
Questions and their Answers
Question 1
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
Question 2
If 0 < t < 2π and sin t = - 1, then t =a) π / 2
b) 3 π / 2
c) 5 π / 4
d) π
Question 3
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
Question 4
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
Question 5
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,...
Question 6
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,...
Question 7
Find all angles θ such that -2π < θ < 2π and cos θ = √2 / 2a) {-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
- d)
- b)
- a)
- d)
- c)
- b)
- a)
