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Class 10 trigonometry worksheet



<1) Write the values  cos 0, cos 45, cos 60 and cos 90. What happens to the values of cos  increases from 0 to 90?
2) Write the values of sin 0, sin 30, sin 45, sin 60 and sin 90. What happens to the values of sin  increases from 0 to 90?
3) Write the values of tan 0, tan 30, tan 45, tan 60 and tan 90. What happens to the values of tan  increases from 0 to 90?
4) If sin A =3/5  find cos A and tan A.
5) If cosec A =√10  find other five trigonometric ratios.
6) In a right triangle ABC right angled at B if sin A =3/5  find all the six trigonometric ratios of <C.
7) The value of (sin30° + cos30°) – (sin60° + cos60°) is
8)  True and False statement
a) The value of sinθ + cosθ is always greater than 1
b) tanθ increases faster than sinθ as θ increase
c) The value of the expression (cos2 23° – sin2 67°) is positive.
d)  The value of the expression (sin 80° – cos80°) is negative.
e) If cosA + cos2A = 1, then sin2A + sin4A = 1.
f). (tan θ + 2) (2 tan θ + 1) = 5 tan θ + sec2θ.
g) If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
h) If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
i) If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged
j) cos4 A – cos2 A = sin4 A – sin2 A
k)cot4 A – 1 = cosec4 A – 2cosec2 A
l) sin4 A + cos4 A = 1 – 2 sin2 A cos2 A
m) sin4 A – cos4 A = sin2 A – cos2 A = 2sin2 A – 1 = 1 – 2 cos2 A
9) If sin B = , show that 3 cos B – 4 cos3 B = 0.
10) If tanA + 1/tanA = 2, find the value of tan2A + 1/tan2A
11) Evaluate the following:
2 sin2 30 - 3cos2 45 + tan2 60
12) Evaluate:
sin2 30 cos2 45 + 4tan2 30 + (1/2) sin2 90- 2 cos2 90 + (1/24) cos2 0
13) Evaluate:
cot2 30 - 2 cos2 60 - (3/4) sec2 45 - 4sec2 30
14) Prove that:
cos 1o cos 2o cos3o…. cos 180o = 0
Answer
4) 2√6/7
5)1/√10,3/√10,1/3,√10/3,3
6) 4/5, 3/5, 4/3, 5/4, 5/3, ¾
7) 0
8)
a) false
b) true
c) false
d) false
e) true
f) false
g) false
h) false
i) true
j) true
k) true
l) true
m) true
9) 1/2
10) 2
11) 2
12) 2
13) -13/3


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