Question

a. in radiansb.in degreesHint:HEARRERANote: You can earn partial credit on this problem.Preview My AnswersSubmit Answers

Answer 1

EXPLANATIONS:

Given;

We are given the following expression;

$arctan(\frac{1}{\sqrt{3}})$

Required;

We are required to find the angle measure of this in both radians, and degrees.

Step-by-step solution;

For the angle whose tangent is given as 1 over square root of 3, on the unit circle, we would have

$\begin{gathered} tan\theta=\frac{1}{\sqrt{3}} \\ Rationalize: \\ \\ \frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ =\frac{\sqrt{3}}{\sqrt{3}\times\sqrt{3}} \\ \\ =\frac{\sqrt{3}}{3} \end{gathered}$

On the unit circle, the general solution for this value as shown would be;

$tan^{-1}(\frac{\sqrt{3}}{3})=\frac{\pi}{6}$

To convert this to degree measure, we will use the following equation;

$\frac{r}{\pi}=\frac{d}{180}$

We now substitute for the value of r;

$\begin{gathered} \frac{\frac{\pi}{6}}{\pi}=\frac{d}{180} \\ \\ \frac{\pi}{6}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ \frac{\pi}{6}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ \frac{1}{6}=\frac{d}{180} \end{gathered}$

We now cross multiply;

$\begin{gathered} \frac{180}{6}=d \\ \\ 30=d \end{gathered}$

Therefore;

ANSWER:

$\begin{gathered} radians=\frac{\pi}{6} \\ \\ degrees=30\degree \end{gathered}$