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24-08-2020
Mathematics

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Find sin(2A) if sin(A)=[tex]\frac{1}{4}[/tex] and [tex]0\leq A\leq \frac{\pi }{2}[/tex]

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MathPhys MathPhys

24-08-2020

Step-by-step 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

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