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Questions in: Trigonometric Functions

Math (11)

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ID: Class: 11 Subject: Math Topic: Trigonometric Functions Type: Short

Question:

Find the value of: \(\sin 75^\circ\)

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Official Solution

Explanation:

We have:
\begin{align*}
\sin 75^\circ &= \sin(45^\circ + 30^\circ) \\
&= \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ \\
&= \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}} \cdot \frac{1}{2} \\
&= \frac{1}{\sqrt{2}} \cdot \left( \frac{\sqrt{3} + 1}{2} \right) \\
&= \frac{\sqrt{3} + 1}{2\sqrt{2}}
\end{align*}

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