Free Printable Math_F.3_Ch09 Trigonometric Relatinoship

1.

4\sin60\degree-\sqrt{3}=

a)

0

b)

$\sqrt{3}$

c)

$2\sqrt{3}$

d)

$3\sqrt{3}$

2.

If $2\cos\theta=\sqrt{2}$ , where θ is an acute angle, then θ =

a)

15°.

b)

30°.

c)

45°.

d)

60°.

3.

Find θ in the figure.

a)

30°

b)

45°

c)

60°

d)

75°

4.

Given that $2\sin\theta=\cos\theta$ , where θ is an acute angle, find the value of $\tan\theta$ .

a)

$\frac{1}{2}$

b)

1

c)

2

d)

$\frac{10}{3}$

5.

$\frac{\cos\theta}{\cos\left(90\degree-\theta\right)}=$

a)

$\tan\theta$

b)

$-\tan\theta$

c)

$\frac{1}{\tan\theta}$

d)

$-\frac{1}{\tan\theta}$

6.

$\tan\theta\sin\left(90\degree-\theta\right)=$

a)

$\sin\theta$

b)

$\cos\theta$

c)

$\frac{\sin^2\theta}{\cos\theta}$

d)

$\frac{\cos\theta}{\sin^2\theta}$

7.

If $\frac{1}{\tan\theta}=\tan36\degree$ , find the acute angle θ.

a)

36°

b)

44°

c)

54°

d)

64°

8.

Which of the following are trigonometric identities?

I.

\tan\left(90\degree-\theta\right)\cos\left(90\degree-\theta\right)=\cos\theta

II.

\frac{1}{\sin\theta}+\frac{1}{\cos\theta}=\frac{1}{\sin\theta\cos\theta}

III.

\frac{\cos\left(90\degree-\theta\right)}{\sin\left(90\degree-\theta\right)}=\tan\theta

a)

I and II only

b)

I and III only

c)

II and III only

d)

I, II and III

9.

Find the value of $\frac{\tan^260\degree}{\sin45\degree}$ .

a)

$\frac{\sqrt{2}}{3}$

b)

$\frac{\sqrt{6}}{2}$

c)

$\sqrt{2}$

d)

$3\sqrt{2}$

10.

If $\sin\theta\tan60\degree=\cos30\degree$ , where θ is an acute angle, then θ =

a)

20°.

b)

30°.

c)

45°.

d)

60°.

11.

In the figure, △ABC is a right-angled triangle where ∠BAC = 90°. D is a point on BC such that $AD\perp BC$ . If BC = 12 cm and ∠ABD = 60°, find the length of AD.

a)

$3\sqrt{3}$ cm

b)

$4\sqrt{3}$ cm

c)

6 cm

d)

$6\sqrt{3}$ cm

12.

If $\tan\theta=\frac{3}{4}$ , find the value of $2\sin\theta-\cos\theta$ .

(θ represents an acute angle.)

a)

$-\frac{1}{5}$

b)

$\frac{1}{4}$

c)

$\frac{1}{3}$

d)

$\frac{2}{5}$

13.

If $\cos\theta=\frac{a}{b}$ , where b > a, then $\tan\theta=$
(θ represents an acute angle.)

a)

$\frac{a}{\sqrt{b^2-a^2}}$

b)

$\frac{b}{\sqrt{b^2-a^2}}$

c)

$\frac{\sqrt{b^2-a^2}}{a}$

d)

$\frac{\sqrt{b^2-a^2}}{b}$

14.

$\frac{1}{\sin^2\theta}-\frac{1}{\tan^2\theta}=$

a)

-1

b)

1

c)

$-\sin\theta$

d)

$-\cos\theta$

15.

If x and y are acute angles and x + y = 90° , then $\sin^2x+\sin^2y=$

a)

0

b)

1

c)

2

d)

$2\sin^2x$

16.

For any acute angles θ, which of the following must be equal to 0?

a)

\left(\cos\theta-\tan\theta\right)^2+2\sin\theta

b)

$\sin^2\theta-\cos^2\theta$

c)

$\tan\left(90\degree-\theta\right)-\tan\ \theta$

d)

$\tan\theta\cos\theta-\sin\theta$

Math_F.3_Ch09 Trigonometric Relatinoship

Total questions: 16

Worksheet time: 4hrs 0mins

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