Answer
a. $ -\frac{336}{625}$
b. $\frac{527}{625}$
c. $ -\frac{336}{527}$
Work Step by Step
Given $cos\theta=\frac{24}{25}$ and $\theta$ in quadrant IV, form a right triangle with sides $7,24,25$. We have $sin\theta=-\frac{7}{25}$ and $tan\theta=-\frac{7}{24}$
a. $sin2\theta=2sin\theta cos\theta=2(-\frac{7}{25})(\frac{24}{25})=-\frac{336}{625}$
b. $cos2\theta=1-2sin^2\theta=1-2(-\frac{7}{25})^2=\frac{527}{625}$
c. $tan2\theta=\frac{sin2\theta}{cos2\theta}=-\frac{336}{527}$
(or use the Double Angle Formula to get the same result.)
