SOLUTION: I need help on this question That sin theta = -1/3 and cos<0, find all 6 trig values for theta.

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Question 882836: I need help on this question
That sin theta = -1/3 and cos<0, find all 6 trig values for theta.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
One of the 6 trigonometric function values, highlight%28sin%28theta%29=-1%2F3%29%29 , is given.
%28cos%28theta%29%29%5E2%2B%28sin%28theta%29%29%5E2=1
%28cos%28theta%29%29%5E2%2B%28-1%2F3%29%5E2=1
%28cos%28theta%29%29%5E2%2B1%2F9=1
%28cos%28theta%29%29%5E2=1-1%2F9
%28cos%28theta%29%29%5E2=8%2F9 ---> system%28cos%28theta%29=sqrt%288%2F9%29%2C%22or%22%2Ccos%28theta%29=-sqrt%288%2F9%29%29
Since cos%28theta%29%3C0 ,
cos%28theta%29=-sqrt%288%2F9%29-->cos%28theta%29=-sqrt%288%29%2Fsqrt%289%29-->highlight%28cos%28theta%29=-2sqrt%282%29%2F3%29%29
csc%28theta%29=1%2Fsin%28theta%29-->csc%28theta%29=1%2F%28-1%2F3%29-->csc%28theta%29=1%2A%28-3%2F1%29-->highlight%28csc%28theta%29=-3%29
sec%28theta%29=1%2Fcos%28theta%29-->sec%28theta%29=1%2F%28-2sqrt%282%29%2F3%29-->sec%28theta%29=-3%2F2sqrt%282%29-->sec%28theta%29=-3sqrt%282%29%2F2sqrt%282%29sqrt%282%29%29-->highlight%28sec%28theta%29=-3sqrt%282%29%2F4%29
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
tan%28theta%29=%28-1%2F3%29%2F%28-2sqrt%282%29%2F3%29-->tan%28theta%29=%28-1%2F3%29%2A%28-3%2F2sqrt%282%29%29-->tan%28theta%29=1%2F2sqrt%282%29%29-->tan%28theta%29=1%2Asqrt%282%29%2F2sqrt%282%29sqrt%282%29%29-->highlight%28tan%28theta%29=sqrt%282%29%2F4%29%29
cot%28theta%29=cos%28theta%29%2Fsin%28theta%29
cot%28theta%29=%28-2sqrt%282%29%2F3%29%2F%28-1%2F3%29-->cot%28theta%29=%28-2sqrt%282%29%2F3%29%2A%28-3%29-->highlight%28cot%28theta%29=2sqrt%282%29%29%29