<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 (cos^{2} 23° – sin^{2} 67°) is positive. d) The value of the expression (sin 80° – cos80°) is negative.
e) If cosA + cos^{2}A = 1, then sin^{2}A + sin^{4}A = 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) cos^{4} A – cos^{2} A = sin^{4} A – sin^{2} A
k)cot^{4} A – 1 = cosec^{4} A – 2cosec^{2} A
l) sin^{4 }A + cos^{4} A = 1 – 2 sin^{2} A cos^{2} A
m) sin^{4 }A – cos^{4} A = sin^{2} A – cos^{2} A = 2sin^{2} A – 1 = 1 – 2 cos^{2} A
9) If sin B = , show that 3 cos B – 4 cos^{3} B = 0.
10) If tanA + 1/tanA = 2, find the value of tan^{2}A + 1/tan^{2}A
11) Evaluate the following:
2 sin^{2} 30 - 3cos^{2} 45 + tan^{2} 60
12) Evaluate:
sin^{2} 30 cos^{2} 45 + 4tan^{2} 30 + (1/2) sin^{2} 90- 2 cos^{2 }90 + (1/24) cos^{2 }0