Posted by **Jon** on Friday, February 15, 2008 at 5:53pm.

Find the exact value of sinx/2 if cosx = 2/3 and 270 < x < 360.

A)1/3

B)-1/3

C)sqrt 6/6

D)-sqrt 6/6

C, since I KNOW cosx is always positive but I don't know the work involved. I know the half angle formula

- Trig -
**drwls**, Friday, February 15, 2008 at 6:08pm
First of all, x/2 will be in the second quadrant, since x is in the fourth quadrant. The sine of x/2 will therefore be positive.

Use the formula for sin (x/2) in terms of cos x.

sin(x/2) = sqrt([1-cos(x)]/2) = sqrt (1/6) = sqrt6/6

You got the right answer, but you it ssmes to have been a lucky guess.

Cos x is NOT always positive, but it is in this case.

- Trig -
**Jon**, Friday, February 15, 2008 at 6:13pm
Thank you. It wasn't really a guess it was either C or D and then I just knew it was positive so that just leaves C.

- Trig -
**Damon**, Friday, February 15, 2008 at 6:20pm
Jon,

Perhaps it would help if you drew an x-y axis system with a unit radius vector in each of the four quadrants.

then in quadrant 1

sin T = y/1 so +

cos T = x/1 so -

tan T = y/x so +

then in quadrant 2

sin T = y/1 so +

cos T = x/1 so - because x is - in q 2

tan T = y/x so -

then in quadrant 3

sin T = y/1 so -

cos T = x/1 so -

tan T = y/x so + because top and bottom both -

then in quadrant 4

sin T = y/1 so -

cos T = x/1 so +

tan T = y/x so -

sin has same sign as its inverse csc

cos has same sign as its inverse sec

tan has same sign as its inverse ctan

- Trig TYPO -
**Damon**, Friday, February 15, 2008 at 6:21pm
then in quadrant 1

sin T = y/1 so +

cos T = x/1 so +

tan T = y/x so +

## Answer This Question

## Related Questions

- Math - For f(x) = 2sinx + (sinx)^3 + tanx find f'(pi/3). Ok, so what I tried was...
- Trig........ - I need to prove that the following is true. Thanks (cosx / 1-sinx...
- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- Trig (Last URGENT) - sin2x+cosx=0 , [-180,180) = 2sinxcosx+cosx=0 = cosx(2sinx+1...
- Precalculus/Trig - I can't seem to prove these trig identities and would really ...
- math - tanx+secx=2cosx (sinx/cosx)+ (1/cosx)=2cosx (sinx+1)/cosx =2cosx ...
- Trigonometry Check - Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [...
- Calculus - Q: If y=sinx/(1+tanx), find value of x not greater than pi, ...
- CALC - 1. The problem statement, all variables and given/known data cos(x) = -2 ...
- Calc - 1. The problem statement, all variables and given/known data cos(x) = -2 ...

More Related Questions