RevisionDojo

SL 3.8—Solving trig equations - IB Questionbank | RevisionDojo

Practice SL 3.8—Solving trig equations 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

SLPaper 1

Consider the function $f(x) = 3 \sin(kx + \frac{\pi}{4}) - 1$

For the function $f(x)$ find the amplitude of the function.

[1]

Determine the value of $k$ such that the $f(x)$ has a period of $12\pi$

[3]

Find the $x$ -coordinates of the minima and maxima of the function $f(x)$ within a period of $12\pi$ and $k>0$ under the domain $x\in[0,2\pi]$

[6]

Question 2

SLPaper 2

Solve the following equations in the interval $0 \leq x \leq \pi$

Note answers have to be rounded up to 4 decimal places.

$\sin 2 x=\frac{1}{3}$

[2]

$\sin ^{2} x=\frac{1}{3}$

[2]

Question 3

SLPaper 1

Solve the following equations in the interval $0^{\circ} \leq x \leq 360^{\circ}$

$\sin 2 x=\frac{1}{2}$

[5]

$\cos 2 x=\frac{\sqrt{3}}{2}$

[5]

Question 4

SLPaper 1

The function
$f(x)=2\sin(2x-\tfrac{\pi}{3})$ is defined for $0\le x\le2\pi$ .

State the amplitude and period of $f$ .

[2]

Determine the $x$ -intercepts of $f$ in the given interval, in exact form.

[3]

Find the coordinates of the first maximum point of $f$ .

[2]

Solve, for $0\le x\le2\pi$ , the equation
$2\sin(2x-\tfrac{\pi}{3})=1.$
Give exact solutions.

[3]

Sketch one full period of $y=f(x)$ , clearly indicating amplitude, period, and intercepts.

[3]

Question 5

SLPaper 1

Consider the equation
$2\cos(2x)=\sin(x)+1, \qquad 0\le x<2\pi.$

Show that the equation may be written as
$4\cos^2x-\sin x-3=0.$

[3]

Express $\cos^2x$ in terms of $\sin x$ , and hence obtain a quadratic equation in $\sin x$ .

[2]

Solve $4\sin^2x+\sin x-1=0$ exactly for $\sin x$ .

[2]

Determine all exact values of $x$ in the given interval that satisfy the original equation.

[5]

Sketch the graphs of $y=2\cos(2x)$ and $y=\sin x+1$ for $0\le x\le2\pi$ on the same axes,
indicating approximate points of intersection corresponding to your algebraic solutions.

[3]

Question 6

SLPaper 1

Write down the general solutions of the equations in degrees and in radians for below :

$\sin x=\frac{\sqrt{2}}{2}$

[1]

$\sin x=\frac{\sqrt{3}}{2}$

[1]

$\sin x=\frac{-1}{2}$

[1]

$\sin x=\frac{-\sqrt{2}}{2}$

[1]

$\sin x=\frac{-\sqrt{3}}{2}$

[1]

Question 7

SLPaper 1

Solve the following equations in radians :

$\cos x=\frac{1}{2}$ , for $0 \leq x \leq 4 \pi$

[4]

$\cos 3 x=\frac{1}{2}$ , for $0 \leq x \leq 2 \pi$

[6]

Question 8

SLPaper 1

Write down the general solutions of the equations in degrees and in radians for below :

$\tan x=\sqrt{3}$

[1]

$\tan x=1$

[1]

$\tan x=\frac{\sqrt{3}}{3}$

[1]

$\tan x=0$

[1]

$\tan x=\frac{-\sqrt{3}}{3}$

[1]

Question 9

SLPaper 1

Write down the general solutions of the equations in degrees and in radians for below :

$\cos x=\frac{\sqrt{2}}{2}$

[1]

$\cos x=\frac{\sqrt{3}}{2}$

[1]

$\cos x=\frac{-1}{2}$

[1]

$\cos x=\frac{-\sqrt{2}}{2}$

[1]

$\cos x=\frac{-\sqrt{3}}{2}$

[1]

Question 10

SLPaper 1

Solve the following equations in the interval $[-\pi, \pi]$

$\tan ^{2} x=3$

[6]

$3 \sin x=\sqrt{3} \cos x$

[3]

SL 3.8—Solving trig equations Questionbank