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
(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
2
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
3
The diagram shows the graph of $y = \sin x$ for $0° \le x \le 360°$ $\sin 30° = 0.5$

Use the graph to solve $\sin x = -0.5$ for $0° \le x \le 360°$
Level 4 · 3 marksTry it