Chapter 13.2, Problem 52PPSE

Solution

i.

To find: The value of given angles using the calculator.

  $0.7660$

Given:

The angles $\cos {40}^{\circ },\cos {400}^{\circ }$ and $\cos \left(-{320}^{\circ }\right)$ .

Calculation:

Substitute the given values in the calculator to obtain the corresponding values.

  $\begin{array}{c}\cos {40}^{\circ }=0.7660\\ \cos {400}^{\circ }=0.7660\\ \cos \left(-{320}^{\circ }\right)=0.7660\end{array}$

Conclusion:

Hence, the value of given angles is $0.7660$ .

ii.

To observe: The similarities in the obtained values.

Angles are coterminal and have the same values.

Given:

The angles $\cos {40}^{\circ },\cos {400}^{\circ }$ and $\cos \left(-{320}^{\circ }\right)$ .

Calculation:

The values of $\cos {40}^{\circ },\cos {400}^{\circ }$ and $\cos \left(-{320}^{\circ }\right)$ are as follows:

  $\begin{array}{c}\cos {40}^{\circ }=0.7660\\ \cos {400}^{\circ }=0.7660\\ \cos \left(-{320}^{\circ }\right)=0.7660\end{array}$

So, from the obtained data, it is clear that all the given angles have the same values. So, it can be concluded that the given angles are coterminal.

Conclusion:

The given angles are coterminal and have the same values.