Trigonometric Graphs & Equations (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

$\mathrm{f}\left(x\right)=p\cos \left(qx\right)$

The amplitude of $\mathrm{f}\left(x\right)$ is 3 and the period is 30°.

Find $\mathrm{f}\left(10\right)$.

Solve the equation $\sin x=-0.75$ for $0^{°}\le x\le 360°$.

Solve the equation  $\tan x=2$  for  $0°\le x\le 360°$ .

$x=$ ........................   or  $x=$ ........................

Solve $3\tan x=-4$ for $0°\le x\le 360°$.  

$x=$.................. or $x=$.................. 

$x°$ is an obtuse angle and $\sin x°=0.43$ .  

Find the value of $x$.  

$x$ = ..............................................

The grid shows the graph of $y=\cos x$ for $0°⩽x⩽360°$.

Solve the equation $3\cos x=1$ for $0°⩽x⩽360°.$

Give your answers correct to 1 decimal place.

.................... and ....................

On the same grid, sketch the graph of $y=\sin x$ for $0°⩽x⩽360°$.

Here is a sketch of $y=\cos x$for values of $x$ from 0° to 360°

$\alpha °$ is an acute angle.

$\cos \alpha °=k$

Circle the value of $\cos (180°–\alpha °)$

Circle the value of $\cos$$(360°+\alpha °)$

The diagram shows the graph of $\mathrm{f}\left(x\right)={\left(\cos x°\right)}^2$ for $0\le x\le 360.$

Write down the amplitude and period of$\mathrm{f}\left(x\right)$.

Amplitude ................................................

Period ................................................

The diagram shows the graph of $\mathrm{f}\left(x\right)=a\cos \left(bx\right)$ for $0\le x\le 360.$

(i) Write down the amplitude and period of$\mathrm{f}\left(x\right)$.

Amplitude ................................................

Period ................................................

[2]

(ii) Write down the value of $a$ and $b$.

[1]

The diagrams show the graph of a function.   Write down the function.

$\mathrm{f}\left(x\right)=$................................................

i) On the axes, sketch the graph of  $y=\sin x$  for  $0°\le x\le 360°.$

[2]

ii) Describe fully the symmetry of the graph of  $y=\sin x$  for  $0°\le x\le 360°.$

[2]

Solve  $4\sin x-1=2$  for  $0°\le x\le 360°.$

$x=$ ........................ and $x=$ ......................

On the diagram, sketch the graph of $y=\cos x$ for $0°\le x\le 360°$.

Solve the equation $4\cos x+2=3$ for $0°\le x\le 360°$.

$x=$ .................... and $x=$ ....................

Solve the equation  $5\tan x=-7$  for  $0°\le x\le 360°$.

     $x=$.................... or $x=$....................

$y$is an obtuse angle.

Which statement is true? Tick one box.