Chapter 4, Problem 6CT

To determine

To Determine:The reference angle ${\theta }^{\text{'}}$ as mentioned in the problem

Answer to Problem 6CT

The reference angle ${\theta }^{\text{'}}$ is ${25}^0$ .

Explanation of Solution

Given information:

The mentioned angle $\theta$ in the problem is ${205}^0$ .

Formula used:

The reference angle ${\theta }^{\text{'}}$ .

If $\theta$ is between ${180}^0$ to ${270}^0$

Then

  $\theta \text{'}=\theta -{180}^0$

Calculation:

Consider the statement “The reference angle ${\theta }^{\text{'}}$ ”.

Recall that the reference angle ${\theta }^{\text{'}}$ is $\theta -{180}^0$ , when

  $\theta$ lies between

  ${180}^{0}to{270}^0$ .

Therefore,$\begin{array}{l}\theta \text{'}=\theta -{180}^0\\ \theta \text{'}={205}^0-{180}^0={25}^0\end{array}$

  $\theta \text{'}={205}^0-{180}^0={25}^0$

So, the reference angle $\theta \text{'}$ is ${25}^0$ .