Question

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

Answer 1

remember the double angle formula:
\[\sin(2A)=2\sin A\cos A\]we already have the \(\sin A\) part and need the cosA.
to get that, we use the identity
\[\sin^2A+\cos^2A=1\] using this, we get two possible values for cosine -> one positive and one negative. Since the angle A is in the first quadrant, cosA must be positive and we take the positive value.
then plug in the numbers and find
sin 2A