SOLUTION: Hello! I need help solving this please: Use the given values to evaluate (if possible) all six trigonometric functions. tan x=1, cos x=- squart2/2 what is sinx and csc

Algebra ->  Trigonometry-basics -> SOLUTION: Hello! I need help solving this please: Use the given values to evaluate (if possible) all six trigonometric functions. tan x=1, cos x=- squart2/2 what is sinx and csc      Log On


   

Question 978428: Hello!
I need help solving this please:
Use the given values to evaluate (if possible) all six trigonometric functions.
tan x=1, cos x=- squart2/2
what is sinx and cscx?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the information given was system%28tan%28x%29=1%2Ccos%28x%29=-sqrt%282%29%2F2%29 ,
that is more information than needed. Very generous!
system%28tan%28x%29=1%2Ccos%28x%29%3C0%29 would have been enough information.

system%28tan%28x%29=1%2Ctan%28x%29=sin%28x%29%2Fcos%28x%29%29 ---> sin%28x%29%2Fcos%28x%29=1 ---> sin%28x%29=cos%28x%29 .
So highlight%28sin%28x%29=cos%28x%29=-sqrt%282%29%2F2%29 gives you 2 of the trigonometric functions.
system%28sec%28x%29=1%2Fcos%28x%29%2Ccos%28x%29=-sqrt%282%29%2F2%29 ---> sec%28x%29=1%2F%28%28-sqrt%282%29%2F2%29%29=-1%282%2Fsqrt%282%29%29 ---> sec%28x%29=-sqrt%282%29 and
system%28csc%28x%29=+1%2Fsin%28x%29%2Csin%28x%29=cos%28x%29%29 ---> csc%28x%29=1%2Fcos%28x%29=-sqrt%282%29 too.
So highlight%28sec%28x%29=csc%28x%29=-sqrt%282%29%29 gives you another 2 trigonometric functions.
Finally, system%28tan%28x%29=1%2Ccot%28x%29=1%2Ftan%28x%29%29 ---> cot%28x%29=1%2F1=1 ,
so highlight%28tan%28x%29=cot%28x%29=1%29 completes the set of 6 trigonometric funcions,
and as a bonus x=45%5Eo%2B180%5Eo=225%5Eo ,
or if you want the angle in radians, x=pi%2F4%2Bpi=5pi%2F4 ,
because sin%28y%29=cos%28y%29=sqrt%282%29%2F2 for the reference angle y=45%5Eo or y=pi%2F4 .