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 1^o cos 2^o cos3^o…. cos 180^o = 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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Class 10 Maths Class 10 Science