Exercises for Question Type 1: Writing trigonometric functions in different ways

Question 1

Skill question

Simplify $- 2 sin (- θ) + 3 sin (π - θ)$ in terms of $sin θ$ .

[3]

Question 2

Skill question

Prove the identity $sin 3 θ = 3 sin θ - 4 sin^{3} θ$ .

[5]

Question 3

Skill question

Simplify $sin (π + θ)$ in terms of $sin θ$ .

[2]

Question 4

Skill question

Express $cos 2 θ$ in terms of $sin θ$ only.

[1]

Question 5

Skill question

Express $sin (- θ)$ using only $sin θ$ .

[1]

Question 6

Skill question

Write $f (θ) = 5 sin θ + 5 cos θ$ in the form $R sin (θ + α)$ , where $R > 0$ and $0 < α < \frac{π}{2}$ .

[5]

Question 7

Skill question

Express $g (x) = sin x + 3 cos x$ in the form $R cos (x - α)$ , where $R > 0$ and $0 < α < \frac{π}{2}$ .

[5]

Question 8

Skill question

Simplify $sin (2 π - θ)$ in terms of $sin θ$ .

[2]

Question 9

Skill question

Express $h (x) = 2 sin 3 x - 2 cos 3 x$ in the form $R sin (3 x - α)$ , where $R > 0$ and $0 < α < \frac{π}{2}$ .

[5]

Question 10

Skill question

Simplify $- sin (\frac{π}{2} + θ)$ in terms of $cos θ$ .

[2]

Question 11

Skill question

Simplify $- 3 sin (3 π - θ)$ in terms of $sin θ$ .

[2]

Question 12

Skill question

Express $cos θ - sin θ$ in the form $2 sin (α - θ)$ , stating the value of $α$ .

[5]

IB Mathematics Analysis and Approaches Question Type 1: Writing Trigonometric Functions in Different Ways Exercises