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

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 $0^{\circ}<x<360^{\circ}$

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.

$\mathrm{cos}α^{\circ}=k$

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

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

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 one statement is true?