SOLUTION: I am having a problem with this question...please don't just give me the answer, I would really like to know how to do it. Thanks f(theta)=3tan(theta)+sin2(theta), find f(pi/6)

Algebra ->  Trigonometry-basics -> SOLUTION: I am having a problem with this question...please don't just give me the answer, I would really like to know how to do it. Thanks f(theta)=3tan(theta)+sin2(theta), find f(pi/6)      Log On


   

Question 262433: I am having a problem with this question...please don't just give me the answer, I would really like to know how to do it. Thanks
f(theta)=3tan(theta)+sin2(theta), find f(pi/6)
Found 2 solutions by drk, jim_thompson5910:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is our equation
f%28theta%29=3tan%28theta%29%2Bsin%5E2%28theta%29
find f(pi/6)
---
step 1 - replace theta with pi/6 and we get
f%28pi%2F6%29+=+3tan%28pi%2F6%29+%2B+sin%5E2%28pi%2F6%29
step 2 - find the values of
3tan(pi/6) and sin^2(pi/6) as
3tan%28pi%2F6%29 = 3*(sqrt(3)/3) = sqrt%283%29
sin%5E2%28pi%2F6%29 = (1/2)^2 = 1%2F4
--
So, we get
f%28pi%2F6%29+=+3tan%28pi%2F6%29+%2B+sin%5E2%28pi%2F6%29
which becomes
f%28pi%2F6%29+=+sqrt%283%29+%2B+1%2F4
----
If however you meant the original problem as:
f%28theta%29=3tan%28theta%29%2Bsin%282%28theta%29%29
then we have
step 1 - replace theta with pi/6 and we get
f%28pi%2F6%29+=+3tan%28pi%2F6%29+%2B+sin%282%28pi%2F6%29%29
step 2 - find the values of
3tan(pi/6) and sin(2(pi/6)) as
3tan%28pi%2F6%29 = 3*(sqrt(3)/3) = sqrt%283%29
sin%282%28pi%2F6%29%29 = sin%28pi%2F3%29 = sqrt%283%29%2F2
--
So, we get
f%28pi%2F6%29+=+3tan%28pi%2F6%29+%2B+sin%282%28pi%2F6%29%29
which becomes
f%28pi%2F6%29+=+sqrt%283%29+%2B+sqrt%283%29%2F2
or
f%28pi%2F6%29+=+3sqrt%283%29%2F2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Plug in and use the unit circle to determine that and . Let me know if this helps you get started.