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

The graph shows $\mathrm{f} ( x ) = a \cos ( b x )^{\circ}$.

Find the value of $a$ and the value of $b$.

Extract:

Oscillating graph on a set of axes, x axis from 0 to 360 and y axis from -3 to 3. Graph goes through the points (0,3), (90,-3), (180,3), (270,-3) and (360,3). The graph shows f(x) = a cos(bx).

Write down the period of $f(x)$.

$\mathrm{f} ( x ) = 3 \sin ( 4 x^{\circ} )$

Find the amplitude and period of $\mathrm{f} ( x )$.

Amplitude = ................................................

Period = ................................................

On the diagram, sketch the graph of $y=\mathrm{tan}x$ for $0^{\circ}\leq x\leq360^{\circ}$.

When $\mathrm{sin}x^{\circ}=0.36$, find the acute angle $x^{\circ}$.

When $\mathrm{sin}x^{\circ}=0.36$, find the obtuse angle $x^{\circ}$.

The diagram shows part of a sketch of the curve $y=\mathrm{sin}x^{\circ}$

Write down the coordinates of

i) the point P

ii) the point Q

Sketch the graph of $y=\mathrm{tan}x$ for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ}$

Show the coordinates of any points of intersection with the coordinate axes.

Sketch the graph of $y = \text{cos} x ^{\circ} \text{for} 0 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360$

Sketch the graph of $y=\mathrm{sin}x$ for $0^{\circ}<x<360^{\circ}$

$\mathrm{f} ( x ) = p \sin ( q x )$

The amplitude of $\mathrm{f} ( x )$ is 4 and the period is 120°.

Find the exact value of $\mathrm{f} ( 45 )$.

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

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

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

Solve the equation $\mathrm{sin}x=-0.75$ for $0^{^{\circ}}\leq x\leq360^{\circ}$.

Solve the equation $\mathrm{tan}x=2$ for $0^{\circ}\leq x\leq360^{\circ}$ .

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

Solve $3\mathrm{tan}x=-4$ for $0^{\circ}\leq x\leq360^{\circ}$.

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

$x^{\circ}$ is an obtuse angle and $\mathrm{sin}x^{\circ}=0.43$ .

Find the value of $x$.

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

The grid shows the graph of $y=\mathrm{cos}x$ for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ}$.

Solve the equation $3\mathrm{cos}x=1$ for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ} .$

Give your answers correct to 1 decimal place.

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

On the same grid, sketch the graph of $y=\mathrm{sin}x$ for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ}$.

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

$α^{\circ}$ is an acute angle.

$\mathrm{cos}α^{\circ}=k$

Circle the value of $\mathrm{cos}(180^{\circ}--α^{\circ})$

Extract:

α° is an acute angle. cos α° = k

Circle the value of $\mathrm{cos}\quad (360^{\circ}+α^{\circ})$

The diagram shows the graph of $\mathrm{f} ( x ) = ( \cos x^{\circ} )^{2}$ for $0\leq x\leq360.$

Write down the amplitude and period of$f(x)$.

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

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

The diagram shows the graph of $\mathrm{f} ( x ) = a \cos ( b x )$ for $0\leq x\leq360.$

(i) Write down the amplitude and period of$f(x)$.

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

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

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

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

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

i) On the axes, sketch the graph of $y=\mathrm{sin}x$ for $0^{\circ}\leq x\leq360^{\circ}.$

ii) Describe fully the symmetry of the graph of $y=\mathrm{sin}x$ for $0^{\circ}\leq x\leq360^{\circ}.$

Solve $4\mathrm{sin}x-1=2$ for $0^{\circ}\leq x\leq360^{\circ}.$

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

On the diagram, sketch the graph of $y=\mathrm{cos}x$ for $0^{\circ}\leq x\leq360^{\circ}$.

Solve the equation $4\mathrm{cos}x+2=3$ for $0^{\circ}\leq x\leq360^{\circ}$.

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

Solve the equation $5\mathrm{tan}x=-7$ for $0^{\circ}\leq x\leq360^{\circ}$.

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

$y$is an obtuse angle.

Which statement is true? Tick one box.