005 Sample Final A, Question 12

From Math Wiki
Jump to navigation Jump to search

Question Given that and , find the exact values of the remaining trig functions.

1) Which quadrant is in?
2) Which trig functions are positive in this quadrant?
3) What are the side lengths of the triangle associated to
1) is in the third quadrant. We know it is in the second or third quadrant since is negative. Since \ is positive is in the third quadrant.
2) and are both positive in this quadrant. All other trig functions are negative.
3) The side lengths are 2, 1, and
Step 1:
Since , we have .
Step 2:
We look for solutions to on the unit circle. The two angles on the unit circle with are and .
But, . Since . we must have .
Step 3:
The remaining values of the trig functions are

Final Answer:

Return to Sample Exam