Question

Find sin(2A) if sin(A)=
`(1)/(4)` and
`0\leq A\leq (\pi )/(2)`

Answer 1

Explanation:

sin(2A)

Use double angle formula:

= 2 sin(A) cos(A)

Use Pythagorean identity. 0 ≤ A ≤ π/2, so cos(A) > 0.

= 2 sin(A) √(1 − sin²(A))

Substitute and simplify.

= 2 (¼) √(1 − (¼)²)

= ½ √(¹⁵/₁₆)

= ⅛ √15