Question

If sin(x) = 2/5 and x is an acute angle, find the exact values of

a) cos(2x)

b) cos(4x)

c) sin(2x)

d) sin(4x)

please answer fast

Answer 1

sinx = 2/5
cosx = √21/5

(a) cos(2x ) = cos²x - sin²x
= 1- 2sin²x
=1 -2 (2/5)²
= 1 - 8/25
=17/25


(b) cos(4x ) = 2cos²(2x) - 1
= 2(17/25)²-1
= 2 × 289/625 - 1
= (578 -625)/625
= -47/625

(c) sin(2x) = 2sinx.cosx
= 2×2/5 × √21/5
=4√21/25

(d) sin(4x) = 2sin2x.cos2x
= 2 × 4√21/25 × 17/25
= 136√21/625