Questions on Solving Simple Trigonometric Equations

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

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 / 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}

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