Chapter 13.4, Problem 50SR

a)

To determine

To find: The value of $\cos (-{30}^{\circ })$

Answer to Problem 50SR

  $\frac{\sqrt{3}}{2}=0.866$

Explanation of Solution

Given information:

We know that, the given expression is Trigonometric ratio $\cos (-{30}^{\circ })$

Formula used:

  $\cos (-\theta )=\cos \theta$

Calculation:

  $\begin{array}{l}\Rightarrow \cos (-{30}^{\circ })\\ \Rightarrow \cos {30}^{\circ }\\ \Rightarrow \frac{\sqrt{3}}{2}\\ \Rightarrow 0.8660\end{array}$

b)

To determine

To find: The value of $\cos ({105}^{\circ })$

Answer to Problem 50SR

  $\frac{1-\sqrt{3}}{2\sqrt{2}}$

Explanation of Solution

Given information:

The given expression is Trigonometric ratio $\cos ({105}^{\circ })$

Formula used:

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

Calculation:

  $\begin{array}{l}\Rightarrow \cos ({105}^{\circ })\\ \Rightarrow \cos ({60}^{\circ }+{45}^{\circ })\\ \Rightarrow \cos {60}^{\circ }\cos {45}^{\circ }-\sin {60}^{\circ }\sin {45}^{\circ }\\ \Rightarrow \frac{1}{2}\times \frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{2}}\\ \Rightarrow \frac{1}{2\sqrt{2}}-\frac{\sqrt{3}}{2\sqrt{2}}\\ =\frac{1-\sqrt{3}}{2\sqrt{2}}\end{array}$