SOLUTION: Please help me solve this problem: Suppose that cot (Beta)= 9/7 and Beta is not in Quadrant I. Find sin(Beta) and cos(Beta). Use fundamental identities, give exact answers and r

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this problem: Suppose that cot (Beta)= 9/7 and Beta is not in Quadrant I. Find sin(Beta) and cos(Beta). Use fundamental identities, give exact answers and r      Log On


   

Question 395071: Please help me solve this problem:
Suppose that cot (Beta)= 9/7 and Beta is not in Quadrant I. Find sin(Beta) and cos(Beta). Use fundamental identities, give exact answers and rationalize if necessary.
Thank you!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have

cos%28beta%29%2Fsin%28beta%29+=+9%2F7%29. This number is positive, so either sine and cosine are both positive or both negative, so the angle is in quadrant III (since it's not in quadrant I).

Hence, cos%28beta%29+=+9%2Fx and sin%28beta%29+=+7%2Fx for some negative number x that we wish to find. By the Pythagorean identity,

81%2Fx%5E2+%2B+49%2Fx%5E2+=+1

130%2Fx%5E2+=+1

x%5E2+=+130

x+=+-sqrt%28130%29 --> cos%28beta%29+=+-9%2Fsqrt%28130%29+=+-9sqrt%28130%29%2F130 and sin%28beta%29+=+-7%2Fsqrt%28130%29+=+-7sqrt%28130%29%2F130.