SOLUTION: find the values of the other five trigonometric functions of theta. sin theta = -7/10, pi < theta < 3pi/2

Algebra ->  Trigonometry-basics -> SOLUTION: find the values of the other five trigonometric functions of theta. sin theta = -7/10, pi < theta < 3pi/2       Log On


   

Question 1080423: find the values of the other five trigonometric functions of theta.

sin theta = -7/10, pi < theta < 3pi/2
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1
cos%5E2%28theta%29%2B49%2F100=1
Solve for cos%28theta%29.
Due to the range given the solution will be negative.
Then,
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
cot%28theta%29=1%2Ftan%28theta%29
sec%28theta%29=1%2Fcos%28theta%29
csc%28theta%29=1%2Fsin%28theta%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the values of the other five trigonometric functions of theta.

sin theta = -7/10, pi < theta < 3pi/2
-------
sin = -7/10 in Q3
cos%28t%29+=+sqrt%281+-+sin%5E2%28t%29%29
cos = -sqrt(51)/10 **** negative in Q3
----
tan = sin/cos = 7sqrt(51)/51
==================
cot = 1/tan
sec = 1/cos
csc = 1/sin