Use a double-angle formula to find the exact value of cos2u when $$\sin u = \frac { 7 } { 25 } \text {, where } \frac { \pi } { 2 }

Question

Use a double-angle formula to find the exact value of cos2u when​ $$\sin u = \frac { 7 } { 25 } \text {, where } \frac { \pi } { 2 } < u < \pi$$
A) $\cos 2 u = \frac { 527 } { 625 }$
B)​ $\cos 2 u = - \frac { 1152 } { 625 }$
C)​ $\cos 2 u = \frac { 336 } { 625 }$
D)​ $\cos 2 u = \frac { 168 } { 625 }$
E)​ $\cos 2 u = - \frac { 478 } { 625 }$

Quizplus · Accepted Answer

The double-angle formula for cosine is $\cos 2u = 2\cos^2u - 1$ or $\cos 2u = 1 - 2\sin^2u$. Given $\sin u = \frac{7}{25}$, we can use $\cos 2u = 1 - 2\sin^2u = 1 - 2\left(\frac{7}{25}\right)^2 = 1 - 2\left(\frac{49}{625}\right) = 1 - \frac{98}{625} = \frac{625 - 98}{625} = \frac{527}{625}$.

Use a Double-Angle Formula to Find the Exact Value of Cos2u