Question

If sin A = 2/3
where 0° < A < 90°, what is the value of sin 2A

Answer 1

1) (2radical5)/3
2)(2radical5)/9
3)(4radical5)/9
4)-(4radical5)/9

Answer 2

2*sin(A)*cos(A)

Answer 3

double angle, what is cos(A) if the sin(A)=2/3?

It is the point (x,y) = (cos(A), Sin(A)) on the unit circle

Answer 4

Recall:
\[\sin^2(A) + \cos^2(A) = 1\]

Answer 5

\[Sin(2A) = 2*Sin(A)*Cos(A)\]

Answer 6

i know that but i am having trouble using this to help me find the correct answer

Answer 7

If you want to find the cosine first, use
\[(2/3)^2 + \cos^2(A) = 1\]
\[\cos(A) = \sqrt{1-4/9} = \sqrt{5/9} = \frac{ \sqrt{5} }{ 3 }\]

Answer 8

Then From double angle
\[Sin(2A) = 2*Sin(A)*Cos(A) = 2*\frac{ 2 }{ 3 }*\frac{ \sqrt{5} }{ 3 }\]

Answer 9

(4radical5)/9?