Trigonometric Graphs & Equations (AQA GCSE Further Maths): Exam Questions

Show that  $2{\cos }^2\theta \equiv 2-2{\sin }^2\theta$

Hence, solve  $2{\cos }^2\theta +3\sin \theta =3$  for  $0<\theta <180°$

Here is a sketch of  $y=\sin x$  for  $0°⩽x⩽360°$

You are given that $\sin 220°=–k$

Work out the two values of$x$for $0°⩽x⩽360°$ for which  $y=k$

Work out the value of $x$ where  $0°⩽x⩽90°$ for which $3{\tan }^{2}x=1$

Here is a sketch graph of $y=\cos x$ for  $0°⩽x⩽360°$

You are given that   $\cos 36°=0.8090$

Solve $\cos x=-0.8090$    for   $0°⩽x⩽360°$

$8\cos x+5\sin x=0$ where $90°<x<180°$

Work out the size of angle $x$.

 ........................ degrees

Prove that  ${\sin }^{2}x-3{\cos }^{2}x\equiv 4{\sin }^{2}x-3$.

Hence, or otherwise, work out the values of $x$ between $0°$and $360°$ for which ${\sin }^{2}x-3{\cos }^{2}x=0$.

Show that $\frac{2\sin x+\cos x}{\tan x}-\frac{1}{\sin x}$ can be written in the form    $a\cos x+b\sin x$

where $a$ and $b$are integers.

Show that $\frac{2{\sin }^{2}x-1+{\cos }^{2}x}{\sin x\cos x}$ is equivalent to tan $x$

Hence solve $\frac{2{\sin }^{2}x-1+{\cos }^{2}x}{\sin x\cos x}=-1$  for  $0°⩽x⩽360°$

Angle $\theta$ is obtuse and $\sin \theta =\frac{\sqrt{11}}{6}$.

Work out the value of $\cos \theta$.

Angle $x$ is acute.

$\tan x=\frac{p+1}{p-1}$ where $p$ is a constant greater than 1

Which of the statements below is correct?

Circle your answer.

$x=45°$       $x<45°$       $x>45°$       $x$ could be any acute angle