Use a Sum or Difference Identity to Find the Exact $\cos 36 ^ { \circ } = \frac { \sqrt { 5 } + 1 } { 4 }$

question 135

Multiple Choice

Use a sum or difference identity to find the exact value.
-Use the exact value $\cos 36 ^ { \circ } = \frac { \sqrt { 5 } + 1 } { 4 }$ and identities to find the exact value of $\sin 36 ^ { \circ }$ .

• A) \(\frac { ( \sqrt { 10 + 2 \sqrt { 5 } } ) ( 10 - 2 \sqrt { 5 } ) } { 5 }\)
• B) \(\sqrt { 5 } + 1\)
• C) \(\frac { \sqrt { 10 - 2 \sqrt { 5 } } } { 4 }\)
• D) \(\frac { \sqrt { 10 - 2 \sqrt { 5 } } } { 8 }\)