Free Printable NCUK Trigonometry

1.

Find the value of x to 2 significant figures.

a)

19 cm

b)

10 cm

c)

12 cm

d)

16 cm

2.

Find the length of NM. Give your answer in the form $4\sqrt{n}$ where $n$ is an integer.

a)

$4\sqrt{7}\$ m

b)

$2\sqrt{7}$ m

c)

$4\sqrt{2}$ m

d)

$4\sqrt{3}$ m

3.

Solve $\tan2\alpha=4$ . $0\degree\le\alpha\le180\degree$

a)

$38\degree,\ 128\degree,\ 218\degree,\ 308\degree$

b)

$-142\degree,-52\degree,\ 38\degree,\ 128\degree$

c)

$38\degree,\ 128\degree$

d)

$24\degree,\ 114\degree$

4.

Solve the equation $5\cos\alpha=-4\$ for $0\le\alpha\le\pi.$ Give your answer to 3 significant figures.

a)

2.49809

b)

2.50

c)

143

d)

120

5.

You are given $\sin\theta=\frac{12}{37}.\$ Without working out the value of $\theta$ , find $\cos\theta$ giving your answer in the form $\frac{m}{n}$ where $m$ and $n$ are integers.

a)

18.9

b)

0.9459

c)

$\frac{30}{37}$

d)

$\frac{35}{37}$

6.

Find AD.

a)

$\sqrt{91}$ cm

b)

$\sqrt{31}$ cm

c)

$91$ m

d)

$72$ cm

7.

$AD=\sqrt{91}cm$ . Find angle ADC.

a)

$58\degree$

b)

$55.3\degree$

c)

$60\degree$

d)

$65.2\degree$

8.

$AD=\sqrt{91}$ cm and angle ADC is $65.2\degree$ . The area of triangle ACD is the same as the area of triangle ABC. FInd angle BAC.

a)

$72\degree$

b)

$77\degree$

c)

$82\degree$

d)

$80\degree$

9.

Find the length of MN.

a)

16.4 cm

b)

21.2 cm

c)

12.3 cm

d)

18.1 cm

10.

Find SR. Give your answer in the form $4\sqrt{k}$ where $k$ is an integer.

a)

$4\sqrt{22}$

b)

$\sqrt{496}$

c)

$\sqrt{352}$

d)

$4\sqrt{31}$

11.

SR = $4\sqrt{31}$ and the areas of the two triangles are equal to each other. Find RQ.

a)

23.1 cm

b)

43.2 cm

c)

21.4 cm

d)

49.2 cm

12.

Solve $\sin2\theta=-\frac{1}{2}$ $\left(0\degree\le\theta\le360\degree\right)$

a)

105, 165, 285, 345 (degrees)

b)

115, 155, 295, 335 (degrees)

c)

-255, -195, -75, -15 (degrees)

d)

-75, -15, 105, 165 (degrees)

13.

Solve the equation cos2θ = -0.766 for 0° ≤ θ ≤ 360° 😎

a)

60, 100, 240, 280 (degrees)

b)

70, 110, 250, 290 (degrees)

c)

20, 60, 200, 240 (degrees)

d)

80, 120, 260, 300 (degrees)

14.

The area of triangle ABC is 66 cm2. Find the value of sinθ, giving your answer in the form m/n where m and n are integers.

a)

11/29

b)

12/37

c)

14/61

d)

13/42

15.

The area of triangle ABC is 66 cm2 and sinθ = 12/37. Without working out the size of angle θ, find cosθ

a)

13/45

b)

12/45

c)

25/37

d)

35/37

16.

The area of triangle ABC is 66 cm2, sinθ = 12/37 and cosθ = 35/37. Find the length of BC.

a)

7.5 cm

b)

4.2 cm

c)

8.1 cm

d)

5.3 cm

17.

The area of triangle ABC is 66 cm2, sinθ = 12/37, cosθ = 35/37 and BC = 7.5 cm. Find the size of angle C.

a)

42.7 (degrees)

b)

53.1 (degrees)

c)

58.1 (degrees)

d)

46.2 (degrees)

18.

The area of triangle ABC is 66 cm2, sinθ = 12/37, cosθ = 35/37, BC = 7.5 cm and the size of angle C is 53.1 degrees. Find the shortest distance from point A to the side BC.

a)

17.6 cm

b)

16.1 cm

c)

18.3 cm

d)

19.2 cm

19.

The area of triangle PQR is 5 cm². Find the values of a.

a)

2 or 3

b)

2

c)

4 or 5

d)

5

20.

cosθ = 1/8. Find the length of MN.

a)

11 m

b)

10 m

c)

12 m

d)

9 m

21.

cosθ = 1/8 an the length of MN is 12 m. Without working out the size of θ, express sinθ in the form $\frac{\sqrt{m}}{n}$ where m and n are integers.

a)

$\sqrt{\frac{71}{9}}$

b)

$\frac{\sqrt{71}}{3}$

c)

$\sqrt{\frac{63}{64}}$

d)

$\frac{\sqrt{63}}{8}$

22.

cosθ = 1/8, the length of MN is 12 m and sinθ = $\frac{\sqrt{63}}{8}$ . Find angle N.

a)

41.4 degrees (0.723 radians)

b)

52.3 degrees (0.913 radians)

c)

60 degrees ( $\frac{\pi}{3}$ radians)

d)

45 degrees ( $\frac{\pi}{4}$ radians)

23.

Solve the equation $\tan3\theta=0.81$ for $0\degree\le\theta\le180\degree$ .

a)

-167, -107, -47, 13, 73, 133 (degrees)

b)

39 degrees

c)

39, 219, 399 (degrees)

d)

13, 73, 133 (degrees)

NCUK Trigonometry

Total questions: 23

Worksheet time: 46mins

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