SOLUTION: Find the exact value of this. Show your work and explain the steps you take to find the value. sec 11pi/3

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of this. Show your work and explain the steps you take to find the value. sec 11pi/3      Log On


   



Question 1029336: Find the exact value of this. Show your work and explain the steps you take to find the value.
sec 11pi/3

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sec%2811pi%2F3%29

Change 11pi%2F3 to degrees:

expr%2811pi%2F3%29%2Aexpr%28%22180%B0%22%2Fpi%29=%22660%B0%22

We subtract 360° enough times to get a
a positive coterminal angle less than 360°: 

660°-360° = 300° (it was only necessary to
subtract 360° one time.)

sec%2811pi%2F3%29=sec%28%22300%B0%22%29

That is in QIV, So to get the reference
angle, we subtract from 360° and get 
360°-300° = 60°.

The secant, which is the reciprocal
of the cosine, and the cosine is +
in QIV, so 

sec%2811pi%2F3%29%22%22=%22%22%22%22%2Bsec%28%2260%B0%22%29%22%22=%22%221%2Fcos%28%2260%B0%22%29%22%22=%22%221%2F%281%2F2%29%22%22=%22%222

Edwin