Free Printable Trigonometry (Intermediate)

1.

Which of the following graphs represent the function $f\left(x\right)=\cos\left(2x\right)$ ?

a)

b)

c)

d)

2.

Which of the following is true?

a)

Sine is positive in the first and third quadrants.

b)

Cosine is negative in the first and fourth quadrants.

c)

Tangent is negative in the second and fourth quadrants.

d)

Sine is negative in the second and third quadrants.

3.

Calculate the value(s) of $\theta$ such that $\cos\left(\theta\right)=-\frac{1}{2}$ for $0\le\theta\le2\pi$ .

a)

$\theta=\frac{2\pi}{3},\frac{4\pi}{3}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3}$

c)

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

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

4.

Calculate the value(s) of $\theta$ such that $\tan\left(2\theta\right)=\sqrt{3}$ for $0\le\theta\le2\pi$ .

a)

$\theta=\frac{\pi}{6},\frac{2\pi}{3}$

b)

$\theta=\frac{\pi}{6},\frac{2\pi}{3},\frac{\ 7\pi}{6},\frac{6\pi}{5}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3},\frac{\ 7\pi}{3},\frac{12\pi}{5}$

d)

$\theta=\frac{\ 7\pi}{6},\frac{6\pi}{5}$

5.

Solve the equation $2\sin\left(\theta\right)=\tan\left(\theta\right)$ for $0^{\circ}\le\theta\le360^{\circ}$ .
Note: Use the fact that $\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$ .

a)

$\theta=0^{\circ},30^{\circ},90^{\circ},150^{\circ},180^{\circ}$

b)

$\theta=0^{\circ},180^{\circ},360^{\circ}$

c)

$\theta=0^{\circ},60^{\circ},180^{\circ},300^{\circ},360^{\circ}$

d)

$\theta=0^{\circ},300^{\circ}$

6.

For $0^{\circ}\le\theta\le360^{\circ}$ , solve $6\cos^2\left(\theta\right)+6\cos\left(\theta\right)-1=0$ .

a)

$\theta=81.6^{\circ},120^{\circ},240^{\circ},278.4^{\circ}$

b)

$\theta=81.6^{\circ},120^{\circ}$

c)

$\theta=240^{\circ},120^{\circ}$

d)

$\theta=81.6^{\circ},\ 278.4^{\circ}$

7.

Solve the equation $\sin^2\left(\theta\right)+3\cos\left(2\theta\right)=2$ for $0\le\theta\le360\degree^{ }$ . Give your answer(s) to 1 decimal place.
Note: Use the fact that $\cos\left(2\theta\right)=1-2\sin^2\left(\theta\right)$

a)

$\theta=153.4^{\circ}$

b)

$\theta=26.6^{\circ}$

c)

$\theta=26.6^{\circ},153.4^{\circ}$

d)

$\theta=26.6^{\circ},153.4^{\circ},206.6^{\circ},333.4^{\circ}$

8.

A right-angled triangle XYZ has an angle, $\theta$ , where $\sin\left(\theta\right)=\frac{\sqrt{5}}{5}$ . Without evaluating $\theta$ , calculate the exact value(in surd form if applicable) of $\cos\left(\theta\right)$ .

a)

$\cos\left(\theta\right)=2\sqrt{5}$

b)

$\cos\left(\theta\right)=\frac{2}{5}$

c)

$\cos\left(\theta\right)=\frac{\sqrt{5}}{5}$

d)

$\cos\left(\theta\right)=\frac{2\sqrt{5}}{5}$

9.

A right-angled triangle XYZ has an angle, $\theta$ , where $\sin\left(\theta\right)=\frac{\sqrt{5}}{5}$ . Without evaluating $\theta$ , calculate the exact value(in surd form if applicable) of $\sin\left(2\theta\right)$ .
Note: Use the fact that $\sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right)$ .

a)

$\sin\left(2\theta\right)=\frac{4}{5}$

b)

$\sin\left(2\theta\right)=\frac{1}{5}$

c)

$\sin\left(2\theta\right)=\frac{2\sqrt{5}}{5}$

d)

$\sin\left(2\theta\right)=\frac{\sqrt{10}}{5}$

10.

A wire in the form of a circle with radius 4 cm is reshaped into the form of a sector of a circle with radius 10 cm. Determine, in radians, the angle of the sector, giving your answer in terms of $\pi$ .

a)

$\theta=\frac{4\pi}{5}-1$

b)

$\theta=\frac{2\left(2\pi-5\right)}{5}$

c)

$\theta=\frac{4\pi}{5}$

d)

$\theta=4\left(2\pi-5\right)$

Trigonometry (Intermediate)

Total questions: 10

Worksheet time: 5mins

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