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 the graph of $y = \sin x$ for $0° \le x \le 360°$ (a) Write down the maximum value of $\sin x$

(b) Write down the three values of $x$ in this range for which $\sin x = 0$
Level 3 · 2 marksTry it
2
The diagram shows the graph of $y = \cos x$ for $0° \le x \le 360°$ (a) Write down the value of $\cos 0°$

(b) Write down the value of $\cos 180°$
Level 3 · 2 marksTry it
3
The diagram shows the graph of $y = \cos x$ for $0° \le x \le 360°$ (a) Write down the values of $x$ for which $\cos x = 0$ in this interval.

(b) Write down the value of $\cos 360°$
Level 3 · 3 marksTry it
4
(a) Explain why the equation $\sin x = 1.2$ has no solutions.

(b) Write down the maximum value of $3\sin x$
Level 4 · 2 marksTry it
5
The diagram shows the graph of $y = \tan x$ for $0° \le x \le 360°$ $\tan 45° = 1$

(a) Use the graph to write down another solution of $\tan x = 1$ for $0° \le x \le 360°$

(b) Explain why $\tan x$ has no value at $x = 90°$
Level 4 · 3 marksTry it

6 more questions on trigonometric graphs

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