SOLUTION: Someone please help solve this? Use the given information to find the exact value of each of the following. a) sin of 2 theta b)cosine of 2 theta c) tan of 2 theta give

Algebra ->  Trigonometry-basics -> SOLUTION: Someone please help solve this? Use the given information to find the exact value of each of the following. a) sin of 2 theta b)cosine of 2 theta c) tan of 2 theta give      Log On


   

Question 915200: Someone please help solve this?
Use the given information to find the exact value of each of the following.
a) sin of 2 theta
b)cosine of 2 theta
c) tan of 2 theta
given sin theta = 6 (sin theta lies in quadrant III)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You seem to have a typo.
Sine and cosine are always between -1 and 1,
so sin%28theta%29 could never be 6.
Also, an angle in quadrant III has a negative sine,
so maybe it was supposed to be sin(theta) = -0.6 .

Given sin%28theta%29=-0.6 ,
we know that %28cos%28theta%29%29%5E2%2B%28sin%28theta%29%29%5E2=1 ,
so %28cos%28theta%29%29%5E2%2B%28-0.6%29%5E2=1-->%28cos%28theta%29%29%5E2%2B0.36=1-->%28cos%28theta%29%29%5E2=1-0.36-->%28cos%28theta%29%29%5E2=0.64-->
Because theta lies in quadrant III,
we know that cos%28theta%29%3C0 ,
so cos%28theta%29=-0.8 .

Now we can apply all those trigonometric identities to find the double angle functions:

a) sin%282theta%29=2sin%28theta%29cos%28theta%29 ,
so sin%282theta%29=2%28-0.6%29%28-0.8%29 --> highlight%28sin%282theta%29=0.96%29

b) cos%282theta%29=%28cos%28theta%29%29%5E2-%28sin%28theta%29%29%5E2 ,
so cos%282theta%29=%28-0.8%29%5E2-%28-0.6%29%5E2 --> cos%282theta%29=0.64-0.36 --> highlight%28cos%282theta%29=0.28%29

c) tan%282theta%29=sin%282theta%29%2Fcos%282theta%29 ,
so tan%282theta%29=0.96%2F0.28 --> highlight%28tan%282theta%29=24%2F7%29
That 24%2F7=%223.428571428571428571+...%22 , with the 428571 repeating forever is the exact value.