SOLUTION: PLEASE HELP ME SOLVE THIS TRIGONOMETRIC FUNCTIONS: Given that sin0=-1/2 and 0 lies in quadrant lV,find the following value.sec 0 the possible answers are: a)-2 b)square root o

Algebra ->  Trigonometry-basics -> SOLUTION: PLEASE HELP ME SOLVE THIS TRIGONOMETRIC FUNCTIONS: Given that sin0=-1/2 and 0 lies in quadrant lV,find the following value.sec 0 the possible answers are: a)-2 b)square root o      Log On


   

Question 237320: PLEASE HELP ME SOLVE THIS TRIGONOMETRIC FUNCTIONS:
Given that sin0=-1/2 and 0 lies in quadrant lV,find the following value.sec 0
the possible answers are:
a)-2
b)square root of 3/2 sqrt%283%2F2%29
c)(2/square root of 3)/3 %282sqrt%283%29%29%2Fsqrt%283%29
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
I am going to replace theta with x since i have no way to make the computer display theta.
So what we have is.
sin%28x%29=-%281%2F2%29
The referance angle that makes sin equal to 1%2F2 is 30 degress or pi%2F6
If we want this angle in the 4th qudrant we get 360-30=330 or 2pi-pi%2F6=11pi%2F6
So we know that our angle is 330 degrees or 11pi%2F6
We also know that sec%28x%29=1%2Fcos%28x%29 So we need to find out what cos(x) is to find sec(x).
So we need to find cos of 330 degrees. The referance angle was 30 degrees and cos%2830%29=sqrt%283%29%2F2. Cos is positive in the 4th quadrent so cos%28330%29=sqrt%283%29%2F2
And sec%28x%29 is 1%2Fcos%28x%29
So sec%28330%29=1%2F%28sqrt%283%29%2F2%29=2%2Fsqrt%283%29
And if you rationalize this.
%282%2Fsqrt%283%29%29%2A%28sqrt%283%29%2Fsqrt%283%29%29=%282sqrt%283%29%29%2F3
So choice C is the correct answer.