GCSE · Graphs of functions

Trigonometric graphsExam-style questions

The sine and cosine waves from 0° to 360° — where they start, peak and cross — why they never leave the band −1 to 1, and how wave symmetry finds the second solution of sin x = k.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
The diagram shows a sketch of the curve with equation $y = \tan x°$ for $0 \le x \le 360$ , together with the lines with equations $y = k$ and $y = -k$ , where $k$ is a positive constant.The line $y = k$ meets the curve at the points $A$ and $B$ .

The line $y = -k$ meets the curve at the points $C$ and $D$ .

The $x$ -coordinate of $A$ is $60$
(a) Find the exact value of $k$ .

(1 mark)
(b) Find the $x$ -coordinate of each of the points $B$ , $C$ and $D$ .

(3 marks)
Level 5 · 4 marksTry it
2
The diagram shows the graph of $y = \sin x$ for $0° \le x \le 360°$ You are given that $\sin 30° = 0.5$

(a) Find the other solution of $\sin x = 0.5$ for $0° \le x \le 360°$

(b) Write down the smallest solution of $\sin x = -0.5$ for $0° \le x \le 360°$
Level 5 · 3 marksTry it
3
The diagram shows the graph of $y = \cos x$ for $0° \le x \le 360°$ You are given that $\cos 60° = 0.5$

Find the other solution of $\cos x = 0.5$ for $0° \le x \le 360°$
Level 5 · 2 marksTry it
4
The diagram shows the graph of $y = \cos x$ for $0° \le x \le 360°$ $\cos 40° = 0.766$ , correct to 3 decimal places.

(a) Use the graph to write down another solution of $\cos x = 0.766$ for $0° \le x \le 360°$

(b) Use the graph to solve $\cos x = -0.766$ for $0° \le x \le 360°$
Level 5 · 3 marksTry it
5
The diagram shows the graph of $y = 2\sin x$ for $0° \le x \le 360°$ (a) Write down the maximum and minimum values of $y = 2\sin x$

(b) Solve $2\sin x = 1$ for $0° \le x \le 360°$
Level 5 · 4 marksTry it