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.