Use an identity to write the expression as a single trigonometric function or as a single number.
-Use the exact value $\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }$ and identities to find the exact value of $\sin 72 ^ { \circ }$.
A) $\frac { ( \sqrt { 10 - 2 \sqrt { 5 } } ) ( 5 + 3 \sqrt { 5 } ) } { 40 }$
B) $\frac { ( \sqrt { 10 - 2 \sqrt { 5 } } ) ( \sqrt { 5 } - 1 ) } { 4 }$
C) $\frac { \sqrt { 10 + 2 \sqrt { 5 } } } { 4 }$
D) $\frac { \sqrt { 10 + \sqrt { 5 } } } { 8 }$

Question

Quizplus · Accepted Answer

The identity $\sin^2 \theta + \cos^2 \theta = 1$ can be used to find $\sin 72^\circ$. Given $\cos 72^\circ = \frac{\sqrt{5} - 1}{4}$, we find $\sin 72^\circ = \sqrt{1 - \cos^2 72^\circ} = \sqrt{1 - \left(\frac{\sqrt{5} - 1}{4}\right)^2} = \frac{\sqrt{10 + 2\sqrt{5}}}{4}$.

Use an Identity to Write the Expression as a Single cos⁡72∘=5−14\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }cos72∘=45​−1​

Use an Identity to Write the Expression as a Single $\cos 72 ^ { \circ } = \frac { \sqrt { 5 } - 1 } { 4 }$