Posted by Sam on Wednesday, October 30, 2013 at 9:32am.
Find the sum of the three smallest positive values of theta such that 4 cos^2(2theta-pi) =3. (Give your answer in radians.)
Hi guys, I've been struggling with this problem. Here's my thinking about the problem:
we can rewrite the equation as cos^2(2theta-pi) = 3/4
Then we sqrt both sides --> cos(2theta - pi) = sqrt3 / 2
we find what arccos sqrt3 / 2 ---> pi/6 radians or 45 degrees (we'll use radians)
thus cos (2theta - pi) = cos(pi/6)
so 2 theta - pi = pi/6
and 2 theta = 7pi/6 ---> 7pi/12
When we let arccos sqrt3/2 ---> 11pi/6 and 13pi/6 we get 17pi/12 and 19pi/12 (those are the smallest two values which are positive, meaning 11pi/6 and 13pi/6)
so in all we get 17pi/12 + 19pi/12 + 7pi/12 = 43pi/12
Is this right?
- Trigonometry - Checking my work - Steve, Wednesday, October 30, 2013 at 11:06am
4cos^2(2θ-pi) = 3
cos^2(2θ-pi) = 3/4
since cos(2θ-pi) - -cos2θ, this makes things simpler, so we have
cos^2 2θ = 3/4
cos2θ = ±√3/2
2θ = π/6,5π/6,7π/6,...
θ = π/12,5π/12,7π/12
Looks like the sum is 13π/12
- Trigonometry - Checking my work - Sam, Wednesday, October 30, 2013 at 11:11am
Oh thanks that helped a lot :)
- Trigonometry - Checking my work - Anonymous, Tuesday, December 15, 2015 at 9:07am
if sinA= 1/3, then find sin (A+pi/6), cos(A-pi/3), tan(A-pi4)
Answer This Question
More Related Questions
- Pre-Calc/ Trig - Find the sum of the three smallest positive values of theta ...
- Math - Trigonometry - For how many values of theta such that 0<theta<360 ...
- Math: Trigonometry - Find the sum of the three smallest positive values of x ...
- Math - The sum of the three smallest positive values of theta such that 4(cos*...
- Math - Trigonometry - Let f(x) be a polynomial such that f(cos theta) = cos(4 ...
- math - There are no typos and no work b/c I don't know how to do them. Thanks. 1...
- Math - sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),...
- trig - given that 1/2pi<theta<pi and sin theta=1/5, use appropriate ...
- Trigonometry - Okay, I have been given a trigonometric equation to solve (sin^2(...
- Precalc Trig - here's the question: solve for cos(2theta)=1 if you graph r= cos(...