SOLUTION: if sec theta=sqrt3 and theta is in the fourth quadrant, find sin theta, cos theta, and tan theta in simplest radical form. please show all work.

Algebra ->  Rational-functions -> SOLUTION: if sec theta=sqrt3 and theta is in the fourth quadrant, find sin theta, cos theta, and tan theta in simplest radical form. please show all work.       Log On


   

Question 952613: if sec theta=sqrt3 and theta is in the fourth quadrant, find sin theta, cos theta, and tan theta in simplest radical form.
please show all work.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sec%28theta%29=sqrt%283%29
cos%28theta%29=1%2Fsec%28theta%29
cos%28theta%29=1%2Fsqrt%283%29
highlight%28cos%28theta%29=sqrt%283%29%2F3%29
.
.
sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1
sin%5E2%28theta%29%2B1%2F3=1
sin%5E2%28theta%29=2%2F3
sin%28theta%29=-sqrt%282%2F3%29
It's negative since sin is negative in the fourth quadrant.
highlight%28sin%28theta%29=-sqrt%286%29%2F3%29
So then,
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
tan%28theta%29=-%28sqrt%286%29%2F3%29%2F%28sqrt%283%29%2F3%29
highlight%28tan%28theta%29=-sqrt%282%29%29