EduSahara™ Worksheet

Question 1

1.

Given that
3

cot

θ

=

4
, find
sin

θ

(i)

3
4
(ii)

3
5
(iii)

5
4
(iv)

5
3
(v)

4
5

Question 2

2.

(i)

12
13
(ii)

13
5
(iii)

13
12
(iv)

5
13
(v)

5
12

Question 3

3.

cot

2°

tan

88°
=

(i)

tan

2°
(ii)

-1
(iii)

tan

88°
(iv)

1
(v)

0

Question 4

4.

Given that
4

cot

θ

=

3
, find
cos

θ

(i)

4
3
(ii)

4
5
(iii)

5
4
(iv)

5
3
(v)

3
5

Question 5

5.

(i)

17
8
(ii)

8
15
(iii)

15
8
(iv)

17
15
(v)

8
17

Question 6

6.

(i)

−

sin

61°
(ii)

−

cos

61°
(iii)

sin

61°
(iv)

cos

61°

Question 7

7.

(i)

4
5
(ii)

5
3
(iii)

5
4
(iv)

4
3
(v)

3
5

Question 8

8.

For angle values from 0° to 90°, which of the following are true?

a)	The tangent value of the angle increases
b)	The sum of the squares of the sine and cosine values remains a constant
c)	The cosine value of the angle increases
d)	The cotangent value of the angle increases
e)	The sine value of the angle increases
f)	The product of the sine and cosine values remains a constant

(i)

{f,c,e}
(ii)

{a,b,e}
(iii)

{d,a,b}
(iv)

{d,b}
(v)

{c,a}

Question 9

9.

(i)

2
13

√

13
(ii)

0
(iii)

1
2

√

13
(iv)

3
13

√

13
(v)

1
3

√

13

Question 10

10.

Express
cos

80°
in terms of
sin

80°

(i)

√

1

−

sin

2

80°

sin

80°

(ii)

1

√

1

−

sin

2

80°
(iii)

1

sin

80°
(iv)

√

1

−

sin

2

80°

(v)

sin

80°

√

1

−

sin

2

80°

Question 11

11.

sec

30°

cosec

3°

cosec

60°

sec

87°
=

(i)

1
(ii)

tan

30°
(iii)

-1
(iv)

0
(v)

tan

3°

Question 12

12.

In the given figure, △GHI is right angled at H. If HI = 9 cm and ∠I = 45°, find GH and GI

(i)
9

cm

&

9

√

2

cm
(ii)
8

cm

&

21

cm
(iii)
10

cm

&

18

cm
(iv)
10

cm

&

21

cm
(v)
10

cm

&

9

√

2

cm

Question 13

13.

In the given figure, △HIJ is a right angle triangle with ∠J = 90° and IJ = 17 cm. P is the mid-point of HJ. Find ∠PIJ using tables.

(i)

37 ° 53 '
(ii)

38 ° 53 '
(iii)

42 ° 53 '
(iv)

40 ° 53 '
(v)

43 ° 53 '

Question 14

14.

From the given figure,
find
cosec

(

90

−

B

)

(i)

BD

CD
(ii)

BD

BC
(iii)

CD

BD
(iv)

CD

BC
(v)

BC

CD

Question 15

15.

(i)

3
4
(ii)

3
5
(iii)

4
5
(iv)

4
3
(v)

5
4

Question 16

16.

In the given figure,
sin

O
=

(i)

5
13
(ii)

5
11
(iii)

1
3
(iv)

7
13
(v)

3
13

Question 17

17.

(i)

(

2

−

√

3

)
(ii)

(

−

1

+

√

3

)
(iii)

(

4

+

√

3

)
(iv)

(

2

+

√

3

)
(v)

(

2

+

3

)

Question 18

18.

If
sec

6

x

=

cosec

(

(

x

+

27

)

)
, then
x
=

(i)

6
(ii)

10
(iii)

9
(iv)

12
(v)

8

Question 19

19.

(i)

4
5
(ii)

3
5
(iii)

4
3
(iv)

5
4
(v)

5
3

Question 20

20.

a)

(

y

+

z

)

2
=
b

2

b)

2

y

z
=
b

2
sin

2

θ

c)

(

y

2

−

z

2

)

=

b

2

d)

(

y

2

+

z

2

)

=

b

2

e)

y

2

z

2
=
tan

2

θ

(i)

{c,d}
(ii)

{a,c,e}
(iii)

{a,b,d}
(iv)

{a,b}
(v)

{b,d,e}

Question 21

21.

Express
cosec

46°
in terms of
cot

46°

(i)

√

1

+

cot

2

46°

cot

46°

(ii)

1

cot

46°

(iii)

cot

46°

√

1

+

cot

2

46°

(iv)

√

1

+

cot

2

46°
(v)

1

√

1

+

cot

2

46°

Question 22

22.

Given that
5

cosec

θ

=

13
, find
tan

θ

(i)

12
5
(ii)

5
13
(iii)

12
13
(iv)

13
12
(v)

5
12

Question 23

23.

sin

18°

−

cos

72°
=

(i)

2

sin

18°
(ii)

0
(iii)

1
(iv)

-1
(v)

2

sin

72°

Question 24

24.

Find the length of the chord of the unit circle subtending an angle of 121° at the centre

(i)

1.7408
(ii)

1.7908
(iii)

1.6408
(iv)

1.8408

Question 25

25.

From Table of Natural Tangents
x°	0'	6'	12'	18'	24'	30'	36'	42'	48'	54'	1'	2'	3'	4'	5'
17	0.3057	0.3076	0.3096	0.3115	0.3134	0.3153	0.3172	0.3191	0.3211	0.3230	3	6	10	13	16

(i)

17 ° 34 '
(ii)

17 ° 44 '
(iii)

17 ° 29 '
(iv)

17 ° 24 '
(v)

17 ° 39 '

Assignment Key