Trigonometry
Angle Sum and Difference, Double Angle and Half Angle Formulas
Find the exact value of:
If sinx = 2/8, find Cos (3x)

3√15/4

Step-by-step explanation:

sin x = 2/8

sinx = 2/8

sin²x = (2/8)² = 2²/8² = 4/64

1- sin²x = 1-4/64 = 64 -4/64 = 60/64 = 15/16

cos x = √(15/16) = √15 /4

3 x cos x = 3 x √15/4 = 3√15/4

Step-by-step explanation:

Notes that:

.

We use sinx to find cosx:

, then

.

Now we use formule for double angle of sin and cos, to find cos2x and sin2x:

Now, we can find cos3x: