Free Printable trigonometry

1.

What is the SINE ratio of any angle in a right triangle

a)

$\frac{\text{adjacent}}{\text{hypotenuse}}$

b)

$\frac{\text{opposite}}{hypotenuse}$

c)

$\frac{\text{opposite}}{\text{adjacent}}$

d)

$\frac{\text{hypotenuse}}{\text{opposite}}$

2.

What is the COSINE ratio of any angle in a right triangle

a)

$\frac{\text{adjacent}}{\text{hypotenuse}}$

b)

$\frac{\text{opposite}}{hypotenuse}$

c)

$\frac{\text{opposite}}{\text{adjacent}}$

d)

$\frac{\text{hypotenuse}}{\text{opposite}}$

3.

What is the TANGENT ratio of any angle in a right triangle

a)

$\frac{\text{adjacent}}{\text{hypotenuse}}$

b)

$\frac{\text{opposite}}{hypotenuse}$

c)

$\frac{\text{opposite}}{\text{adjacent}}$

d)

$\frac{\text{hypotenuse}}{\text{opposite}}$

4.

In the diagram, S is the midpoint of PQ. If $\tan x=\frac{2}{5}$ and $PR=10\ cm$ , then $\tan y=$

a)

$\frac{5}{8}$

b)

$\frac{4}{5}$

c)

$\frac{5}{4}$

d)

$\frac{5}{2}$

5.

In the diagram, find the value of $\sin\theta$ .

a)

$\frac{5}{8}$

b)

$\frac{8}{13}$

c)

$\frac{5}{12}$

d)

$\frac{2}{3}$

6.

$Co\sec\ \theta=\ ?$

a)

$\frac{1}{\sin\theta}$

b)

$\frac{1}{\cos\theta}$

c)

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

7.

$Sec\ \theta=\ ?$

a)

$\frac{1}{\sin\theta}$

b)

$\frac{1}{\cos\theta}$

c)

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

8.

$Cot\ \theta=\ ?$

a)

$\frac{1}{\sin\theta}$

b)

$\frac{1}{\cos\theta}$

c)

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

9.

Simplify $\frac{\cos^2\theta}{1-\sin\theta}$

a)

$\cos\theta$

b)

$\tan^2x$

c)

$1+\sin\theta$

d)

$1-\sin\theta$

10.

$\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}$ simplify

a)

$1-\sin\theta$

b)

$1+\sin\theta$

c)

$\cos\theta$

d)

$\sec\theta\operatorname{cosec}\theta$

11.

Simplify $\frac{1+\tan^2\theta}{\operatorname{cosec}^2\theta}$

a)

$\sin\theta$

b)

$\frac{1}{\cos\theta}$

c)

$\tan^2\theta$

d)

$\frac{1}{\sin\theta}$

12.

$\frac{\cos^2X}{\sqrt[]{1-\sin^2X}}$ simplify

a)

$\cos\theta$

b)

$\cos X$

c)

$1-\sin X$

d)

$\sin X$

13.

If $\sin\theta=\frac{4}{5},\ 90\degree<\theta<180\degree,\$ find the value of $\cos2\theta$

a)

$-\frac{24}{25}$

b)

$-\frac{7}{25}$

c)

$\frac{7}{25}$

d)

$\frac{24}{7}$

14.

Solve the equation $\cos\theta=\frac{1}{2}$ for $0\le\theta\le2\pi$

a)

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

b)

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

c)

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

d)

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

15.

Solve the equation $\tan\theta=-1$ for $0\degree\le\theta\le360\degree$

a)

$\theta=45\degree,\ 135\degree$

b)

$\theta=135\degree,315\degree$

c)

$\theta=45\degree,135\degree,153\degree$

d)

$\theta=135\degree,135\degree,513\degree$

16.

Solve the equation $\sin2\theta=\frac{1}{2}\$ for $0\degree\le\theta\le360\degree$

a)

$\theta=15\degree,75\degree,195\degree,255\degree$

b)

$2\theta=30\degree,150\degree,390\degree,510\degree$

c)

$\theta=15\degree,75\degree$

d)

$2\theta=15\degree,75\degree,195\degree,255\degree$

17.

Solve the equation $\cos\theta=\cos^2\theta$ for $0\degree\le\theta\le360\degree$

a)

$\theta=90\degree,270\degree$

b)

$\theta=0\degree,30\degree,60\degree,90\degree$

c)

$\theta=0\degree,90\degree,270\degree,360\degree$

d)

$\theta=0\degree,270\degree$

18.

Solve $2\sin^2\theta-3\sin\theta-2=0$ for $0\le\theta\le2\pi$

a)

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

b)

$\theta=\frac{7}{6}\pi,\frac{11}{6}\pi$

c)

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

d)

$\theta=\frac{5}{7}\pi,\frac{11}{5}\pi$

19.

Solve $\sin\theta\cos\theta=-\frac{1}{4}$ for $0\le\theta\le2\pi$

a)

$\theta=\frac{7}{12}\pi,\frac{11}{12}\pi$

b)

$\theta=\frac{12}{7}\pi,\frac{19}{12}\pi$

c)

$\theta=\frac{7}{12}\pi,\frac{11}{12}\pi,\frac{12}{19}\pi,\frac{12}{23}\pi,\frac{23}{12}\pi$

d)

$\theta=\frac{7}{12}\pi,\frac{11}{12}\pi,\frac{19}{12}\pi,\frac{23}{12}\pi$

20.

By using the substitution $t=\tan\frac{\text{}x}{\text{2}}$ solve the equation $1-\sin x=2\cos x$ for $0\degree\le x\le360\degree$

a)

$x=0\degree,67.4\degree,360\degree$

b)

$x=90\degree,323.1\degree$

c)

$x=90\degree,322.1\degree$

d)

$x=0\degree,67.4\degree$

21.

Solve $5\cos\theta+3\sin\theta+5=0$ for $0\degree\le\theta\le360\degree$

a)

$\theta=30.96\degree,180\degree$

b)

$\theta=180\degree,241.9\degree$

c)

$\theta=30.96\degree,180\degree$

d)

$\theta=30.96\degree,241.9\degree$

22.

Solve $\sin^2\theta=\frac{3}{4}\$ for $0\le\theta\le2\pi$

a)

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

b)

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

c)

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

d)

$\theta=\frac{\pi}{3},\frac{2}{3}\pi,\frac{4}{3}\pi,\frac{5}{3}\pi$

23.

Solve $\cos2\theta+\sin\theta=0$ , where $0\degree\le\theta\le360\degree$

a)

$\theta=30\degree,90\degree$

b)

$\theta=90\degree,210\degree,330\degree$

c)

$\theta=90\degree,210\degree$

d)

$\theta=210\degree,330\degree$

24.

Solve $\tan x=\frac{3}{2}$ for $0\degree\le x\le360\degree$

a)

$x=56.31\degree$

b)

$x=56.31\degree,236.31\degree$

c)

$x=55.3\degree,234\degree$

d)

$x=56.31\degree,235.3\degree$

25.

Antara berikut yang tidak mempunyai sudut rujukan sepadan $50\degree$ ?

a)

$130\degree$

b)

$230\degree$

c)

$300\degree$

d)

$310\degree$

26.

Diberi kos θ = –0.454 dan 0° < θ < 360°, hitung sudut θ.

a)

63^o

b)

243^o

c)

297^o

d)

333^o

27.

Tentukan sukuan dan sudut rujukan sepadan bagi sudut 244°

a)

sukuan II, 64°

b)

sukuan III, 64°

c)

sukuan IV, 64°

d)

sukuan I, 64°

28.

Diberi kos θ = –0.454 dan 0° < θ < 360°, hitung sudut θ.

It is given that cos θ = –0.454 and 0° < θ < 360°,

find the angle of θ.

a)

63^o

b)

243^o

c)

297^o

d)

333^o

29.

Tentukan sukuan dan sudut rujukan sepadan bagi sudut 244°

a)

sukuan II, 64°

b)

sukuan III, 64°

c)

sukuan IV, 64°

d)

sukuan I, 64°

30.

Nilai untuk kos 128° berdasarkan sudut rujukan sepadan.

The value of cos 128 ° based on corresponding reference angle.

a)

0.6157

b)

-0.6157

c)

0.788

d)

$-0.788$

31.

cari setiap nilai berikut tanpa menggunakan kalkulator

sin 120

a)

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

b)

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

c)

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

d)

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

32.

Nyatakan sama ada nilai bagi setiap nisbah trigonometri yang berikut adalah 'positif' atau 'negatif'

a) $\tan\ 132\degree$

b)

kos\ 202\degree

c)

\sin\ 333\degree

a)

a) negatif b) negatif c) negatif

b)

a) negatif b) positif c) negatif

c)

a) negatif b) negatif c) positif

d)

a) positif b) negatif c) negatif

e)

a) positif b) positif c) positif

33.

What is the green side labelled as using the starred angle as a starting point?

a)

adjacent

b)

opposite

c)

hypotenuse

34.

What is the green side labelled as from the starred angle?

a)

adjacent

b)

opposite

c)

hypotenuse

35.

From ∠C, what side is AB?

a)

Adjacent

b)

Hypotenuse

c)

Opposite

36.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

37.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

38.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

39.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

40.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

41.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

42.

Find x.

a)

28.9

b)

61.1

c)

64.2

d)

25.8

43.

Find x.

a)

41.8

b)

48.2

c)

33.7

44.

Find x.

a)

42.9

b)

21

c)

33.3

d)

21.9

45.

Find x.

a)

8.5

b)

31.9

c)

8.8

d)

34.2

46.

Find x.

a)

15.8

b)

12.3

c)

25.6

d)

15.6

47.

Find x.

a)

38.7

b)

32

c)

58

d)

51.3

48.

Find x.

a)

2.3

b)

5.6

c)

9.8

d)

11

49.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

50.

Solve for x.

a)

10

b)

11.3

c)

12.0

d)

15.0

51.

cos B = ?

a)

12/13

b)

12/5

c)

5/13

d)

5/12

52.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

53.

What is the correct ratio?

a)

20/12

b)

12/20

c)

12/16

d)

16/12

54.

What is the correct equation to solve for x ?

a)

tan (58) = x/11

b)

tan (58) = 11/x

c)

cos (58) = x/11

d)

sin (58) = x/11

55.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

56.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

57.

What is the correct equation to solve for x?

a)

tan (45) = x/13

b)

cos (45) = x/13

c)

sin (45) = 13/x

d)

sin (45) = x/13

58.

What is the correct equation to solve for x ?

a)

tan( 46 ) = 17/x

b)

sin ( 46 ) = x/17

c)

tan (46 ) = x/17

d)

cos (46) = x/17

59.

Solve for x.

a)

10

b)

11.3

c)

12.0

d)

15.0

60.

Solve for x.

a)

30°

b)

45°

c)

60°

d)

90°

61.

Solve for x.

a)

30°

b)

45°

c)

60°

d)

90°

62.

Find the exact value of x.

a)

√29

b)

√7

c)

7

d)

10

63.

Find the value of x.

a)

15√5

b)

5√5

c)

5√3

d)

3√5

64.

What if the value of x?

a)

16

b)

12

c)

4

d)

64

65.

Find the value of x.

a)

2√7

b)

7√2

c)

√28

d)

28

66.

What is the length of the hypotenuse?

a)

16

b)

30

c)

34

67.

What is the green side labelled as using the starred angle as a starting point?

a)

adjacent

b)

opposite

c)

hypotenuse

68.

What is the green side labelled as from the starred angle?

a)

adjacent

b)

opposite

c)

hypotenuse

69.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

70.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

71.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

trigonometry

Total questions: 71

Worksheet time: 2hrs 29mins

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