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 < 2? such that sin t = √2 / 2 and cot t < 0, then t = ?
a) ? / 4
b) 5 ? / 4
c) 7 ? / 4
d) 3 ? / 4

Question 2

If 0 < t < 2? and sin t = - 1, then t =
a) ? / 2
b) 3 ? / 2
c) 5 ? / 4
d) ?

Question 3

If - 2? < t < 0 and sin t = - 1 / 2, then t =
a) -5 ? / 6
b) -7 ? / 6
c) - 5 ? / 4
d) - 5 ? / 3

Question 4

If 0 < ? < ? and cos ? = -√3 / 2, then ? =
a) ? / 6
b) - ? / 6
c) 7 ? / 6
d) 5 ? / 6

Question 5

Find all values of t such that sin(t) = 0.
a) t = k?/2 ; k = 0, ą 1, ą 2, ą 3,...
b) t = k?/4 ; k = 0, ą 1, ą 2, ą 3,...
c) t = k? ; k = 0, ą 1, ą 2, ą 3,...
d) t = 2 k? ; k = 0, ą 1, ą 2, ą 3,...

Question 6

Find all values of t such that cos(? t) = 1.
a) t = 2 k ? ; k = 0, ą 1, ą 2, ą 3,...
b) t = 2 k ; k = 0, ą 1, ą 2, ą 3,...
c) t = k ; k = 0, ą 1, ą 2, ą 3,...
d) t = k ? ; k = 0, ą 1, ą 2, ą 3,...

Question 7

Find all angles ? such that -2? < ? < 2? and cos ? = √2 / 2
a) {-7 ? / 4, - ? / 4 , ? / 4 , 7 ? / 4}
b) {- ? / 4, - 3 ? / 4 , ? / 4 , 3 ? / 4}
c) {-5 ? / 4, ? / 4 , 3 ? / 4}
d) {? / 4 , ? / 4 , 3 ? / 4}