Chapter 4, Problem 1RE

a.

To determine

To sketch: the angle $\frac{15\pi }{4}$ in standard position.

Answer to Problem 1RE

  

Explanation of Solution

Concept Used:

Radian to degree conversion:

Multiply radians by $\frac{180°}{\pi \text{ radian}}$

First convert the angle from $\frac{15\pi }{4}$ radians into degrees using above formula.

  $\begin{array}{c}\frac{15\pi }{4}=\frac{15\pi }{4}\times \frac{180°}{\pi }\\ =675°\end{array}$

Now, $675°=360°+215°$

The sketch of the angle $\frac{15\pi }{4}$ in standard position is given below:

b.

To determine

the quadrant in which the angle lies

Answer to Problem 1RE

Quadrant IV

Explanation of Solution

From the sketch obtained in the part (a), it can be said that the given angle lies in the Quadrant IV.

c.

To determine

two co terminal angles (one positive and one negative).

Answer to Problem 1RE

  $\frac{23\pi }{4}$ , $-\frac{\pi }{4}$

Explanation of Solution

To find the positive co terminal angle, add $2\pi$ to the given angle.

  $\frac{15\pi }{4}+2\pi =\frac{23\pi }{4}$

To find the negative co terminal angle, subtract $2\pi$ two times from the given angle.

  $\frac{15\pi }{4}-2\pi =\frac{7\pi }{4}$

  $\frac{7\pi }{4}-2\pi =-\frac{\pi }{4}$