Question

Find sin2A if sinA=1/4 and 0<=A<=(pi/2) ...i took precalculus last year and forget how to do this so an explanation would be great

Answer 1

Well, you know that sine is opp/hyp. So you have 4 as the hypotenuse and 1 and the opposite. Use pythagorean's theorem to find the 3rd side the "adj" side. You have 4^2-1^2=a^2
a=sqrt(15)
You also know that:
\[\sin(2A)=2\sin(A)\cos(A)\]
Well cosine is adj/hyp so you have:
\[2*\frac{1}{4}*\frac{\sqrt{15}}{4}=\frac{\sqrt{15}}{8}\]

Answer 2

ohhhh i get it thankkk you

Answer 3

use
sin2A = 2sinA*cosA
and to get cos use \[\sin ^{2}A + \cos ^{?}A=1\]
since sinA = 1/4 by using
\[\sin ^{2}A + \cos ^{2}A = 1\]
\[ 1/16 + \cos ^{2}A = 1\]
\[cosA =\sqrt{16/16 - 1/16}= \sqrt{15/16}\]

\[2\sin a.\cos a = 2 * 1/4 * \sqrt{15}/4 = \sqrt{15}/8\]