Concept Check Match each angle in Column I with its reference ang...

Question

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1.

I.                                  II.
5.                                A. 45°
6.                                B. 60°
7. -135°                      C. 82°
8.                                D. 30°
9.                                E. 38°
10.                              F. 32°

Accepted Answer

Hey, everyone here, we are asked to determine the reference angle of negative 113 degrees. Here we are given four answer choice options, answer choice, a 67 degrees. Answer B 23 degrees. Answer is C 113 degrees and answer D negative 113 degrees. So before we determine the reference angle of our given angle, we first want to find a positive conterminal angle by adding 360 degrees to negative degrees. And so we have negative 113 degrees plus 360 degrees. And now just summing our two values, we get the coat terminal angle degrees. And so now we want to notice that 247 degrees is within 180 degrees as well as 270 degrees. So this tells us that 247 degrees or our given angle, negative 113 degrees, all of these angles are in the third quadrant. And now we just need to recall that for an angle theta which lies in the third quadrant the reference angle is theta minus 180 degrees. And here our theta is 247 degrees. So just solving for our reference angle, we have 247 degrees minus 180 degrees. And now just simplifying, we get 67 degrees as our reference angle. And so we are left with answer choice. A where again, we have 67 degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. -135° C. 82° 8. D. 30° 9. E. 38° 10. F. 32°