Chapter 6, Problem 1CLT

(a)

To determine

To find: The sketch for the angle in the standard position.

Explanation of Solution

Given:

The angle is $\theta =-150°$ .

Calculation:

The sketch for the angle $\theta =-150°$ is shown in Figure 1

  

Figure 1

The angle $\theta =-150°$ sill start from the angel $0$ and will go in clockwise direction to the fourth quadrant.

(b)

To determine

To find: The conterminal angle in the interval $\left[0°,360°\right]$ .

Answer to Problem 1CLT

The value of the conterminal angle is $210°$ .

Explanation of Solution

Given:

The required interval of the co terminal angle is $\left[0°,360°\right]$ .

Calculation:

The conterminal angle in the range $\left[0°,360°\right]$ is,

  $360°-150°=210°$

(c)

To determine

To find: The radian measure of the given angle.

Answer to Problem 1CLT

The radian measure is $\frac{-5\pi }{6}$ .

Explanation of Solution

Given:

The given angle is $\theta =-150°$ .

Calculation:

The value of the angle in the radian measure is,

  $-150°=\frac{-5\pi }{6}$

(d)

To determine

To find: The value of reference angle.

Answer to Problem 1CLT

The value of reference angle is $30°$ .

Explanation of Solution

Given:

The given angle is $\theta =-150°$ .

Calculation:

The value of the reference angle is,

  $\begin{array}{c}{\theta }^{\prime }=180°-150°\\ =30°\end{array}$

(e)

To determine

To find: The exact value of the six trigonometric functions.

Answer to Problem 1CLT

The angle measure for the different trigonometric function is $\sin \left(-150°\right)=\frac{-1}{2}$ , $\cos \left(-150°\right)=\frac{\sqrt{3}}{2}$ , $\tan \left(-150°\right)=\frac{1}{\sqrt{3}}$ , $\cos \text{ec}\left(-150°\right)=-2$ and $\cot \left(-150°\right)=\sqrt{3}$ .

Explanation of Solution

Given:

The given angle is $\theta =-150°$ .

Calculation:

The angle measure for the sine trigonometric function is,

  $\sin \left(-150°\right)=\frac{-1}{2}$

The angle measure for the cosine trigonometric function is,

  $\cos \left(-150°\right)=\frac{\sqrt{3}}{2}$

The angle measure for the tan trigonometric function is,

  $\begin{array}{c}\tan \left(-150°\right)=\frac{\sqrt{3}}{3}\\ =\frac{1}{\sqrt{3}}\end{array}$

The angle measure for the cosec trigonometric function is,

  $\cos \text{ec}\left(-150°\right)=-2$

The angle measure for the sec trigonometric function is,

  $\sec \left(-150°\right)=-\frac{2\sqrt{3}}{3}$

The angle measure for the cot trigonometric function is,

  $\cot \left(-150°\right)=\sqrt{3}$