Chapter 12.4, Problem 1ST

a.

To determine

To find two angles, one positive and one negative, that are conterminal with the given angle.

Answer to Problem 1ST

Positive conterminal angle of the given angle is ${250}^{\circ }+{360}^{\circ }={610}^{\circ }$

Negative conterminal angle of the given angle is ${250}^{\circ }-{360}^{\circ }=-{110}^{\circ }$

Explanation of Solution

Given information :

  ${250}^{\circ }$

When we add ${360}^{\circ }$ to an angle it does not changes its position on the graph.(when the angle is counterclockwise).

Hence positive conterminal angle of the given angle is ${250}^{\circ }+{360}^{\circ }={610}^{\circ }$

Now when we subtract ${360}^{\circ }$ from the angle, the position still remains same.

Hence negative conterminal angle of the given angle is ${250}^{\circ }-{360}^{\circ }=-{110}^{\circ }$

b.

To determine

To find two angles, one positive and one negative, that are conterminal with the given angle.

Answer to Problem 1ST

Positive conterminal angle of the given angle is $-{300}^{\circ }+{360}^{\circ }={60}^{\circ }$

Negative conterminal angle of the given angle is $-{300}^{\circ }-{360}^{\circ }=-{660}^{\circ }$

Explanation of Solution

Given information :

  $-{300}^{\circ }$

When we add ${360}^{\circ }$ to an angle it does not changes its position on the graph.(when the angle is counterclockwise).

Hence positive conterminal angle of the given angle is $-{300}^{\circ }+{360}^{\circ }={60}^{\circ }$

Now when we subtract ${360}^{\circ }$ from the angle, the position still remains same.

Hence negative conterminal angle of the given angle is $-{300}^{\circ }-{360}^{\circ }=-{660}^{\circ }$