SOLUTION: how do I find all the trig function values of theta for : cot(theta)=(-3/4), csc(theta)=(5/4)

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Question 1099073: how do I find all the trig function values of theta for :
cot(theta)=(-3/4), csc(theta)=(5/4)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You have an angle, theta that has
system%28cot%28theta%29=%28-3%2F4%29%2C+csc%28theta%29=%285%2F4%29%29 .
All the trigonometric functions can be calculated from sine and cosine.
csc%28theta%29=1%2Fsin%28theta%29 , so you have 1%2Fsin%28theta%29=5%2F4 ---> highlight%28sin%28theta%29=4%2F5%29

cot%28theta%29=cos%28theta%29%2Fsin%28theta%29 , so you have cos%28theta%29%2Fsin%28theta%29=-3%2F4 , or cos%28theta%29%2F%28%284%2F5%29%29=-3%2F4 ---> cos%28theta%29=%28-3%2F4%29%2A%284%2F5%29 ---> highlight%28cos%28theta%29=-3%2F5%29 .

To complete the half-dozen trigonometric functions, the other two are
sec%28theta%29=1%2Fcos%28theta%29 and tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 or tan%28theta%29=1%2Fcot%28theta%29 , so

sec%28theta%29=1%2F%28-3%2F5%29 ---> highlight%28sec%28theta%29=-5%2F3%29 , and

tan%28theta%29=1%2F%28-3%2F4%29 ---> highlight%28tan%28theta%29=-4%2F3%29 .