SOLUTION: Hello. Please help me solve this. Determine the formula with the correct sign for cos (x/2) if sec x=-5/3, 3pi less than or equal to x less than 7pi/2. I set up the equ

Algebra ->  Trigonometry-basics -> SOLUTION: Hello. Please help me solve this. Determine the formula with the correct sign for cos (x/2) if sec x=-5/3, 3pi less than or equal to x less than 7pi/2. I set up the equ      Log On


   

Question 949025: Hello.
Please help me solve this.
Determine the formula with the correct sign for cos (x/2) if sec x=-5/3, 3pi less than or equal to x less than 7pi/2.
I set up the equation:
++cos%28x%2F2%29=sqrt+%28+1+%2B+-3%2F5%29%2F2++
I simplified that to get sqrt5/5.
Am I on the right track?
Thank you!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Correct track, up to showing the formula, the half-angle formula for cosine.
The cosine is -3%2F5. Quadrant 3, according to part of your description.

Because quadrant 3, cosine(x/2) is NEGATIVE.
cos%28x%2F2%29=-sqrt+%28+1+%2B+-3%2F5%29%2F2

The algebra to do is very elementary.

-sqrt%285%2F5-3%2F5%29%2F2
-sqrt%282%2F5%29%2F2
-%281%2F2%29sqrt%282%29%2F%28sqrt%285%29%29
RATIONALIZE THE DENOMINATOR.
-%281%2F2%29%28sqrt%282%29%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29
-%281%2F2%29%28sqrt%282%29sqrt%285%29%29%2F5
highlight%28-sqrt%2810%29%2F10%29