You are here:

Calculus/u-substitution in trigonmetric equations involving sin, cos, and tan

Advertisement

Expert: - 1/11/2009


Question
Hi.  I have been struggling a bit in my trig class trying to understand u-substitution.  An example of the type of equation that trips me up is:

4sin^2(theta)=1

I can get as far as theta=pi/6 but I don't know where to go from there. my teacher wants us to find the location(s) on the unit circle and she said something about adding 2*pi*K to the answer.  Can you please explain to me what I am supposed to do and if I am even doing it right?  Thanks!

Answer
We know that sin(Θ) = 1/2, so you're right in saying that Θ=π/6.
If you know what the sin(x) curve looks like, it start at 0,
goes up to 1 at π/2 radians, back to 0 at π radians,
down to -1 at 3π/2 radians, and back to 0 at 2π radians.

On the interval (0,π), it is symmetric about π/2.
Our answer, π/6 radians, is π/3 radians below π/2.
Another answer would be π/3 radians above π/2,
which would be 5π/6 radians.

Overall, the solution would be π/6 + 2kπ or 5π/6 + 2kπ radians with k as an integer.

This is because if you add 2π radians to an angle, it comes back around to the same angle since there are 2π radians in a circle.

I'm not sure you really need to find the other angle
(in this case, 5π/6), but adding on 2kπ for some integer k brings the answer around the circle back to the same angle.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.