Chapter 14.4, Problem 37HP

To determine

To Find:The exact value of $\sin {15}^{\circ }$ and identify file error.

Answer to Problem 37HP

Both explanations are wrong. Right answer is $0.2588$

Explanation of Solution

Given information:

We know that, the given expression isTwo- Explanations of $\sin {15}^{\circ }$

Formula used:

  $\sin (A-B)=\sin A\cos B-\cos A\sin B$

Calculation:

  $\begin{array}{l}\Rightarrow \sin ({15}^{\circ })\\ \Rightarrow \cos ({45}^{\circ }-{30}^{\circ })\\ \Rightarrow \sin {45}^{\circ }\cos {30}^{\circ }-\cos {45}^{\circ }\sin {30}^{\circ }\\ \Rightarrow \frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\times \frac{1}{2}\\ \Rightarrow \frac{1.732-1}{2\times 1.414}=\frac{0.732}{2.828}\\ \Rightarrow 0.2588\end{array}$