SOLUTION: Given sin(a)=-{{{1/3}}} in quadrant IV, find the exact values of the other five trig functions.

Algebra ->  Trigonometry-basics -> SOLUTION: Given sin(a)=-{{{1/3}}} in quadrant IV, find the exact values of the other five trig functions.       Log On


   

Question 678258: Given sin(a)=-1%2F3 in quadrant IV, find the exact values of the other five trig functions.
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
In quadrant IV, sine is negative and cosine is positive.
%28sin%28a%29%29%5E2+%2B+%28cos%28a%29%29%5E2+=+1
%28-1%2F3%29%5E2+%2B+%28cos%28a%29%29%5E2+=+1
1%2F9+%2B+%28cos%28a%29%29%5E2+=+1
%28cos%28a%29%29%5E2+=+8%2F9
cos%28a%29+=+2sqrt%282%29%2F3
Now tangent:

Cotangent:

Secant:
sec%28a%29+=+1%2Fcos%28a%29+=+3%2F%282sqrt%282%29%29+=+3sqrt%282%29%2F4
Cosecant:
csc%28a%29+=+1%2Fsin%28a%29+=+-3