trigonometry help!!!!!!!!!!!!!!!!

Question

x is an angle in quadrant 3 and sin (x) = 1 / 3. Find sin (3x) and cos (3x).

Answer 1

The given trigonometric fuction value is sin(x) = 1/3

sin(3x) = 3sinx - 4sin³x

= 3 ( 1/3) - 4 ( 1/3)³

=  - 4 ( 1/27)  =  - 4/27.

sin (x) = 1/3 ⇒ sin²x = 1/9

sin²x + cos²x  = 1

⇒ cos²x  = 1 - sin²x

Therefore cosx = √8/9

cos(3x) = 4 cos³x - 3 cosx

= 4 (√8/3) ³- 3 ( √8/3 )

= 4 ( 8√8/27) - √8

= ( 32/27 -1) √8

= 5/27√8 = 10 √2/27.