Find the exact value. $\sin 75 ^ { \circ }$
A) $\sqrt { 6 } + \sqrt { 2 }$
B) $\sqrt { 6 } - \sqrt { 2 }$
C) $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$
D) $\frac { \sqrt { 6 } + 3 \sqrt { 2 } } { 4 }$
E) $\frac { \sqrt { 6 } + \sqrt { 2 } } { 2 }$

Question

Quizplus · Accepted Answer

The exact value of $\sin 75^\circ$ can be found using the angle addition formula: $\sin(75^\circ) = \sin(45^\circ + 30^\circ) = \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ$. This simplifies to $\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4} = \frac{\sqrt{6} + \sqrt{2}}{4}$.

Find the Exact Value sin⁡75∘\sin 75 ^ { \circ }sin75∘ A) 6+2\sqrt { 6 } + \sqrt { 2 }6​+2​

Find the Exact Value $\sin 75 ^ { \circ }$ A) $\sqrt { 6 } + \sqrt { 2 }$