Question

What is the exact value of sin(2 theta) if cos theta =3/5 and is in quadrant IV?

Answer 1

quadrant IV is quadrant 4 which is the one in the bottom right hand corner

Answer 2

we have:
\[\Large \sin \theta = - \sqrt {1 - {{\left( {\cos \theta } \right)}^2}} = - \sqrt {1 - \frac{9}{{25}}} = ..?\]

Answer 3

the minus sign takes account that we are in the IV quadrant, where sin x is negative.
So we have to apply this formula:
\[\Large \sin \left( {2\theta } \right) = 2\sin \theta \times \cos \theta = ...?\]