Trigonometric functions

The diagram depicts a regular hexagon $ABCDEF$ with side length 10 cm.

Feb/March 2017

The diagram has axes labelled with $0^\circ, 90^\circ, 180^\circ, 270^\circ$ and $360^\circ$ on the x-axis.

Feb/March 2020

Sketch y = \tan x for $0^\circ \leq x \leq 360^\circ$.

Feb/March 2023

Sketch the graph of $y = \cos x$ over $0^\circ \le x \le 360^\circ$.

Feb/March 2024

Solve the equation $2 + 5 \cos x = 0$ for $0^\circ \le x \le 360^\circ$.

Feb/March 2025

Calculate $\sqrt{\frac{1}{2}(1 - \cos 48^{\circ})}$.

May/June 2017

Use a calculator to calculate $\sqrt{1-(\sin 33^{\circ})^2}$.

May/June 2019

The diagram displays a regular pentagon $ABCDE$ drawn inside a circle with centre $O$ and radius 12 cm. $M$ is the midpoint of $BC$. $OMX$ and $ABX$ are straight lines. NOT TO SCALE.

May/June 2019

Sketch $y=\tan x$ over the domain $0^\circ \leq x \leq 360^\circ$.

May/June 2021

Find every solution of $4\sin x = 3$ for $0^\circ \leq x \leq 360^\circ$.

May/June 2021

The diagram shows a pair of axes, with $x$ marked from $0$ to $360$ and $y$ marked from $-1$ to $1$.

May/June 2022

Solve the equation $3\sin x + 3 = 1$ for $0^{\circ} \le x \le 360^{\circ}$.

May/June 2022

From the diagram, sketch the graph of $y = \cos x$ for $0^\circ \leq x \leq 360^\circ$.

May/June 2023

For $0^{\circ} \le x \le 360^{\circ}$, Solve the equation $5\sin x = -3$.

May/June 2023

Solve the equation $8\sin x + 6 = 1$ for values of $x$ in the interval $0^\circ \le x \le 360^\circ$.

May/June 2024

The diagram depicts a right-angled triangle drawn to no scale. Its hypotenuse measures 14 cm, the base measures 8.5 cm, and the angle at the base is $x^\circ$.

May/June 2024

For the sketch, place a ring around the function type shown: linear, cubic, quadratic, reciprocal or exponential.

May/June 2024

Solve for the values of $x$ in the range $0^\circ \leq x \leq 360^\circ$ that satisfy $\tan x + \sqrt{3} = 0$.

May/June 2024

For the circle with centre $O$, the minor arc $PQ$ has length $\frac{3}{7}$ of the major arc $PQ$. Show that $x = 108$.

May/June 2024

The diagram contains two separate right-angled triangles that share one side. It includes angles of 30^{\circ}, with side length $n$ and hypotenuse $x$. Diagram not to scale.

May/June 2025

Draw the graph of $y = \sin x$ for $0^\circ \le x \le 360^\circ$.

May/June 2025

Calculate – $2^3 - \sqrt{10 + 4^2}$.

Oct/Nov 2016

$x^\circ$ is an obtuse angle, and $\sin x^\circ = 0.43$. Find $x$.

Oct/Nov 2018

Given that $\sin x^\circ = 0.36$, find

Oct/Nov 2019

Solve the equation $\tan x = 2$ within $0^\circ \leq x \leq 360^\circ$.

Oct/Nov 2020

Solve $3\tan x = -4$ for $0^\circ \le x \le 360^\circ$.

Oct/Nov 2020

Solve $3(2 + \cos x) = 5$ for values of $x$ on $0^{\circ} \le x \le 360^{\circ}$.

Oct/Nov 2021

Solve $7\sin x + 2 = 0$ for values of $x$ in the interval $0^{\circ} \le x \le 360^{\circ}$.

Oct/Nov 2021

A pair of axes is displayed, with the $x$-axis extending from $0^{\circ}$ to $360^{\circ}$ and the $y$-values spanning from $-1$ to $1$.

Oct/Nov 2022

An axis diagram is displayed with $x$ running from 0 to 360 and $y$ running from -1 to 1.

Oct/Nov 2022

The diagram has $0^\circ$ to $360^\circ$ labelled along the $x$-axis, while the $y$-axis is scaled from $-1$ up to $1$.

Oct/Nov 2022

The diagram shows axes with $0^{\circ}$ to $360^{\circ}$ on the $x$-axis and values from $-1$ to $1$ on the $y$-axis.

Oct/Nov 2023

Work with the function $y=3\cos 2x^\circ$.

Oct/Nov 2023

The diagram depicts two right-angled triangles $PQS$ and $RQT$. $PQR$ and $QTS$ lie on straight lines. The diagram gives: $PS = 18$ cm; angle at $P$ is $28^\circ$; $SQ$ is vertical with a right angle at $Q$; $ST = 4$ cm; $QR = 9$ cm. NOT TO SCALE.

Oct/Nov 2024

Solve the equation $3\tan x + 5 = 1$ for values of $x$ in the interval $0^\circ \leq x \leq 360^\circ$.

Oct/Nov 2024

Find the solutions of $\tan x + 2 = 0$ for $0^\circ \leq x \leq 360^\circ$.

Oct/Nov 2024

Solve $\tan x=\frac{1}{\sqrt3}$ over $0^{\circ}\le x\le360^{\circ}$.

Oct/Nov 2025

Using the diagram, draw the graph of $y=\cos x$ for $0^{\circ}\leq x\leq360^{\circ}$.

Oct/Nov 2025