Trigonometric Graphs & Equations Practice Questions

On the axes, sketch the graph of $y = \cos x$ for $0° \leqslant x \leqslant 360°$

Write down the coordinates of the minimum point of $y = \cos x$ in the interval $0° \leqslant x \leqslant 360°$

Write down the number of solutions of $\cos x = 0.6$ in the interval $0° \leqslant x \leqslant 360°$

On the axes, sketch the graph of $y = \tan x$ for $0° \leqslant x \leqslant 360°$

Write down the equations of the two asymptotes of $y = \tan x$ in the interval $0° \leqslant x \leqslant 360°$

Write down the value of

(i) $\sin 145°$

(ii) $\sin 215°$

Complete the table to show whether each value is positive or negative.

Value	Positive or negative?
$\sin 290°$
$\cos 340°$
$\tan 200°$

Solve $5\cos x = -2$ for $0° \leqslant x \leqslant 360°$

Give your answers to 1 decimal place.

Solve $3\sin x = 2\cos x$ for $0° \leqslant x \leqslant 360°$

Give your answers to 1 decimal place.

Simplify fully $\dfrac{\sin\theta}{\tan\theta}$

Simplify fully $\dfrac{1 - \cos^2\theta}{\tan^2\theta}$

Work out the exact value of $\sin\theta$

Hence write down the exact value of $\tan\theta$

Solve $\sin^2 x = \dfrac{1}{4}$ for $0° \leqslant x \leqslant 360°$

Solve $\tan^2 x = 3\tan x$ for $0° \leqslant x \leqslant 360°$

Give your answers to 1 decimal place where appropriate.

Solve $2\sin^2 x + 3\cos x = 3$ for $0° \leqslant x \leqslant 360°$

Prove that $\tan\theta\sin\theta + \cos\theta \equiv \dfrac{1}{\cos\theta}$