Question

find the degree measures of the next two positive and the previous two negative angles that are coterminal with the angle 218°.

the next two positive coterminal angles are 578.938 °
(use a comma to separate answers as needed. type an integer or a decimal. do not use commas in the individual numbers. type your answer in degrees. do not include the degree symbol in your answer.)

the previous two negative coterminal angles are □°
(use a comma to separate answers as needed. type an integer or a decimal. do not use commas in the individual numbers. type your answer in degrees. do not include the degree symbol in your answer.)

Explanation:

Step1: Recall coterminal angle formula

Coterminal angles are found by adding or subtracting \(360^\circ\) (or \(2\pi\) radians, but here we use degrees). For a given angle \(\theta\), coterminal angles are \(\theta + 360^\circ n\), where \(n\) is an integer.

Step2: Find first negative coterminal angle

To find negative coterminal angles, we use \(n=-1\) and \(n = - 2\) (for two previous negative angles). For \(n=-1\):
\(218^\circ+360^\circ\times(- 1)=218^\circ - 360^\circ=-142^\circ\)

Step3: Find second negative coterminal angle

For \(n = - 2\):
\(218^\circ+360^\circ\times(-2)=218^\circ-720^\circ=-502^\circ\)

Answer:

-142, -502

(Note: For the positive coterminal angles, the given 578.938 seems incorrect. The correct next two positive coterminal angles should be \(218 + 360=578\) and \(218+720 = 938\). Maybe there was a typo in the given number. But following the problem's request for negative angles, we calculated the two previous negative coterminal angles as -142 and -502.)