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AHL 3.11—Relationships between trig functions - IB Questionbank | RevisionDojo

Practice AHL 3.11—Relationships between trig functions with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 1

Evaluate: $\int_0^{\pi} \cos(\pi - x) \, dx.$

[3]

Question 2

HLPaper 1

Consider the following trigonmetric expression

\sin(x+y)-\sin(x-y)

Show that the expression equal to $2\cos(x)\sin(y)$

[3]

Hence, using mathematical induction and the above identity, prove that $\sum_{r=1}^{n} \cos((2r-1)\alpha) = \frac{\sin(2n\alpha)}{2\sin\alpha}$ for $n \in \mathbb{Z}^+$ .

[8]

Question 3

HLPaper 1

Solve the equation in the interval $[0,2 \pi]$

$3 \csc ^{2} x=4$

[5]

Question 4

HLPaper 1

Solve the equation in the interval $[-\pi, \pi]$

$\sin \left(x+\frac{\pi}{3}\right)=2 \cos \left(x-\frac{\pi}{6}\right)$

[5]

Question 5

HLPaper 1

Solve the equation in the interval $[0, \pi]$

$\cos 5 x=\cos 3 x$ ,

[6]

Explain why $\cos (\pi-x)=-\cos x$

[2]

Hence, solve the equation $\cos 5 x+\cos 3 x=0$ , in the interval $[0, \pi][6]$

[6]

Question 6

HLPaper 1

Solve the equation in the interval $[0,4 \pi]$

$\sin x=\sin \frac{x}{3}$

[6]

Question 7

HLPaper 1

Solve the equation $\tan \left(3 \pi x-\frac{\pi}{4}\right)=\tan \pi x$ in the interval $[0,2]$

$\tan \left(3 \pi x-\frac{\pi}{4}\right)=\tan \pi x$ in the interval $[0,2]$

[6]

Question 8

HLPaper 1

Solve the equation in the interval $\left[0, \frac{\pi}{2}\right]$

$\tan x+\cot x=2$ ,

[3]

Question 9

HLPaper 1

Solve the equation in the interval $[0, \pi]$

$\tan 5 x=\tan 3 x$

[4]

Explain why $\tan (-x)=-\tan x$

[1]

Hence, solve the equation $\tan 5 x+\tan 3 x=0$ , in the interval $\left[0, \frac{\pi}{2}\right][6]$

[6]

Question 10

HLPaper 1

The angle $\theta$ satisfies the equation $2 \tan ^{2} \theta-5 \sec \theta-10=0$ , where $\theta$ is in the second quadrant.

Find the exact value of $\sec \theta$ .

[4]

AHL 3.11—Relationships between trig functions Questionbank