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Any angle trigonometry function example

Question:

Given: sin (9pi/2 + a) = 1/5. Find the value of cos a.

Solution:

sin (9pi/2 + a)
= sin [(8pi + pi)/2 + a]
= sin (4pi + pi/2 + a)
= sin (pi/2 + a)
= cos a
= 1/5

Because sin (9pi/2 + a) = 1/5 and sin (9pi/2 + a) = cos a. So, cos a = 1/5. Watch the video for more details.