EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
cos
(
360
+
θ
)
=
cos
θ
b)
tan
(
360
+
θ
)
=
cot
θ
c)
sin
(
360
+
θ
)
=
cos
θ
d)
sin
(
360
+
θ
)
=
sin
θ
e)
tan
(
360
+
θ
)
=
tan
θ
f)
cos
(
360
+
θ
)
=
sin
θ
(i)
{c,d}
(ii)
{c,a,d}
(iii)
{b,a}
(iv)
{a,d,e}
(v)
{f,b,e}
Question
2
2.
Given
sin
N
=
5
13
,
find
sec
N
(i)
13
12
(ii)
13
5
(iii)
5
12
(iv)
12
13
(v)
12
5
Question
3
3.
Express
sin
θ
in terms of
cosec
θ
(i)
cosec
θ
√
cosec
2
θ
−
1
(ii)
1
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
cosec
θ
(iv)
1
cosec
θ
(v)
√
cosec
2
θ
−
1
Question
4
4.
Express
sec
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
tan
θ
√
1
+
tan
2
θ
(iv)
1
tan
θ
(v)
1
√
1
+
tan
2
θ
Question
5
5.
Which of the following are true?
a)
cosec
(
270
−
θ
)
=
−
cosec
θ
b)
cosec
(
270
−
θ
)
=
−
sec
θ
c)
sec
(
270
−
θ
)
=
−
sec
θ
d)
cot
(
270
−
θ
)
=
tan
θ
e)
sec
(
270
−
θ
)
=
−
cosec
θ
f)
cot
(
270
−
θ
)
=
cot
θ
(i)
{c,b,d}
(ii)
{a,b}
(iii)
{c,d}
(iv)
{f,a,e}
(v)
{b,d,e}
Question
6
6.
Which of the following are true?
a)
sin
(
180
−
θ
)
=
cos
θ
b)
sin
(
180
−
θ
)
=
sin
θ
c)
tan
(
180
−
θ
)
=
−
cot
θ
d)
tan
(
180
−
θ
)
=
−
tan
θ
e)
cos
(
180
−
θ
)
=
−
sin
θ
f)
cos
(
180
−
θ
)
=
−
cos
θ
(i)
{a,b}
(ii)
{c,b,d}
(iii)
{c,d}
(iv)
{b,d,f}
(v)
{e,a,f}
Question
7
7.
Given
tan
J
=
1
3
√
3
,
find
sin
J
(i)
2
3
√
3
(ii)
1
2
(iii)
√
3
(iv)
2
(v)
1
2
√
3
Question
8
8.
Find the value of
cos
64
°
12
'
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
64
0.4384
0.4368
0.4352
0.4337
0.4321
0.4305
0.4289
0.4274
0.4258
0.4242
3
5
8
11
13
(i)
0.4349
(ii)
0.4355
(iii)
0.4356
(iv)
0.4352
(v)
0.4348
Question
9
9.
Which of the following are true?
a)
cot
90°
is not defined
b)
cosec
90°
is not defined
c)
sec
90°
is not defined
d)
sec
0°
is not defined
e)
tan
90°
is not defined
f)
cosec
0°
is not defined
g)
tan
0°
is not defined
h)
cot
0°
is not defined
(i)
{b,e}
(ii)
{a,c}
(iii)
{a,h,c}
(iv)
{c,e,f,h}
(v)
{d,g,f}
Question
10
10.
Express
tan
θ
in terms of
cos
θ
(i)
cos
θ
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
1
cos
θ
(v)
1
√
1
−
cos
2
θ
Question
11
11.
Express
cosec
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
tan
θ
(iv)
1
tan
θ
(v)
1
√
1
+
tan
2
θ
Question
12
12.
The value of
sin
356°
in terms of an angle between
0°
and
90°
is
(i)
cos
86°
(ii)
−
cos
86°
(iii)
sin
86°
(iv)
−
sin
86°
Question
13
13.
Given that
3
tan
θ
=
4
, find
cos
θ
(i)
5
3
(ii)
5
4
(iii)
3
4
(iv)
4
5
(v)
3
5
Question
14
14.
In the given figure, △IKJ is right angled at J. If IJ = 21 cm and ∠K = 60°, find KL
(i)
7
2
cm
(ii)
21
4
√
2
cm
(iii)
7
2
√
3
cm
(iv)
7
2
√
18
cm
(v)
21
2
cm
Question
15
15.
Given that
4
tan
θ
=
3
, find
cot
θ
(i)
4
3
(ii)
4
5
(iii)
3
5
(iv)
5
4
(v)
5
3
Question
16
16.
Express
sin
θ
in terms of
sec
θ
(i)
1
√
sec
2
θ
−
1
(ii)
1
sec
θ
(iii)
√
sec
2
θ
−
1
sec
θ
(iv)
√
sec
2
θ
−
1
(v)
sec
θ
√
sec
2
θ
−
1
Question
17
17.
cos
64°
sin
80°
sin
26°
cos
10°
=
(i)
tan
80°
(ii)
1
(iii)
-1
(iv)
tan
64°
(v)
0
Question
18
18.
Given
cot
M
=
3
4
,
find
cosec
M
(i)
4
3
(ii)
3
5
(iii)
5
4
(iv)
5
3
(v)
4
5
Question
19
19.
In
△FGH
, right angled at
G
,
if
tan
F
=
2
3
,
find
cos
F
cos
H
−
sin
F
sin
H
(i)
1
2
√
13
(ii)
0
(iii)
1
3
√
13
(iv)
2
13
√
13
(v)
3
13
√
13
Question
20
20.
cosec
57°
sec
33°
=
(i)
0
(ii)
tan
33°
(iii)
-1
(iv)
1
(v)
tan
57°
Question
21
21.
Express
tan
80°
in terms of
cos
80°
(i)
cos
80°
√
1
−
cos
2
80°
(ii)
1
cos
80°
(iii)
1
√
1
−
cos
2
80°
(iv)
√
1
−
cos
2
80°
(v)
√
1
−
cos
2
80°
cos
80°
Question
22
22.
Given that
4
sec
θ
=
5
, find
cos
θ
(i)
5
3
(ii)
3
5
(iii)
4
3
(iv)
4
5
(v)
3
4
Question
23
23.
The value of
sin
194°
in terms of an angle between
0°
and
90°
is
(i)
−
sin
14°
(ii)
cos
14°
(iii)
sin
14°
(iv)
−
cos
14°
Question
24
24.
Given
sin
H
=
3
5
,
find
tan
H
(i)
3
4
(ii)
5
3
(iii)
4
5
(iv)
4
3
(v)
5
4
Question
25
25.
If
tan
θ
−
cot
θ
=
3
, find
tan
2
θ
+
cot
2
θ
(i)
9
(ii)
14
(iii)
10
(iv)
12
(v)
11
Assignment Key
1) (iv)
2) (i)
3) (iv)
4) (i)
5) (v)
6) (iv)
7) (ii)
8) (iv)
9) (iv)
10) (iii)
11) (iii)
12) (ii)
13) (v)
14) (iii)
15) (i)
16) (iii)
17) (ii)
18) (iii)
19) (ii)
20) (iv)
21) (v)
22) (iv)
23) (i)
24) (i)
25) (v)
