Free Printable Ch 7 Trigonometric functions

1.

What is $80\degree$ in radians?

a)

$\frac{\pi}{80}$

b)

$\frac{4\pi}{9}$

c)

$\frac{\pi}{8}$

d)

$\frac{2\pi}{9}$

2.

Which one of the following is a solution of the equation $2\cos x=1$ ?

a)

$\frac{5\pi}{3}$

b)

$\frac{4\pi}{3}$

c)

$\pi$

d)

$\frac{2\pi}{3}$

3.

What are the amplitude and period of the function $y=2\sin\frac{1}{2}\pi x$ ?

a)

amplitude $2$

period $4\pi$

b)

amplitude $2$

period $1$

c)

amplitude $\pi$

period $\frac{\pi}{2}$

d)

amplitude $2$

period $4$

4.

The diagram shows the line $y=\frac{1}{2}x+\frac{1}{4}$ intersecting the curve $y=\sin x$ in three distinct points.

How many positive solutions does the equation $4\sin x=2x+1$ have?

a)

$0$

b)

$1$

c)

$2$

d)

$3$

5.

What is the derivative of $x\sin2x$ ?

a)

$\cos2x+2x\sin2x$

b)

$2\cos2x$

c)

$\sin2x$

d)

$\sin2x+2x\cos2x$

6.

What is the gradient of the curve $y=\tan^3x$ at the point where $x=\frac{\pi}{3}$ ?

a)

$36$

b)

$12\ \sqrt[]{3}$

c)

$12$

d)

$9$

7.

What is the equation of the normal to $y=x\sin x$ at the point where $x=\frac{\pi}{3}$ ?

a)

$y+\frac{\pi\ \sqrt[]{3}}{6}=\frac{6}{3\ \sqrt[]{3}+\pi}\left(x+\frac{\pi}{3}\right)$

b)

$y-\frac{\pi\ \sqrt[]{3}}{6}=-\frac{6}{3\ \sqrt[]{3}+\pi}\left(x-\frac{\pi}{3}\right)$

c)

$y+\frac{\pi\ \sqrt[]{3}}{6}=\frac{3\ \sqrt[]{3}+\pi}{6}\left(x+\frac{\pi}{3}\right)$

d)

$y-\frac{\pi\ \sqrt[]{3}}{6}=\frac{3\ \sqrt[]{3}+\pi}{6}\left(x-\frac{\pi}{3}\right)$

8.

Which function is a primitive of $2\cos2x-3\sin x$ ?

a)

$2\sin2x-3\cos x$

b)

$\sin2x+3\cos x$

c)

$2\sin2x+3\cos x$

d)

$\sin2x-3\cos x$

9.

A sketch of the function $y=\sin2x$ is shown.

Given that $\int_0^{\frac{\pi}{4}}\sin2x\ dx=\frac{1}{2}$ , what is the value of $\int_0^{2\pi}\sin2x\ dx$ ?

a)

$2$

b)

$0$

c)

$4$

d)

$1$

10.

What is the area of the region shaded in the diagram?

a)

$\frac{1}{2}\left(\sqrt[]{3}-1\right)$ square units

b)

$1$ square unit

c)

$\left(\sqrt[]{2}-1\right)$ square units

d)

$\sqrt[]{2}$ square units

11.

The line y = mx is a tangent to the curve y = cosx at the point where x = a, as shown in the diagram.

Which of the following statements is true?

a)

$m<\frac{1}{a}<\frac{1}{2\pi}$

b)

$\frac{1}{2\pi}<m<\frac{1}{a}$

c)

$\frac{1}{2\pi}<\frac{1}{a}<m$

d)

$m<\frac{1}{2\pi}<\frac{1}{a}$

12.

Which interval gives the range of the function $y=5+2\cos3x$ ?

a)

$\left[2,\ 8\right]$

b)

$\left[3,\ 7\right]$

c)

$\left[4,\ 6\right]$

d)

$\left[5,\ 9\right]$

Ch 7 Trigonometric functions

Total questions: 12

Worksheet time: 24mins

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