Having Trouble: Solving a Trigonometric Equation using Identities ?

1. Jun 30, 2011

nukeman

Having Trouble: Solving a Trigonometric Equation using Identities ???

1. The problem statement, all variables and given/known data

I am having problems with these. Need some help please!!

Here is a sample question I am having troubles with:

3 cos θ + 3 = 2 sin^2 θ, 0 <= θ < 2pi

I am really struggling with these. Any help would be great. What is my first step for solving a Trigonometric Equation using Identities ?

2. Relevant equations

3. The attempt at a solution

My teacher said you can solve this with a ti89 - But how would that be even possible? Just curious.

Thanks

2. Jun 30, 2011

Staff: Mentor

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

I wouldn't even bother with a calculator, at least at first. Use the identity sin2x + cos2x = 1 to convert the sin2θ term, and then you will have an equation that is quadratic in form, in cosθ. Use the quadratic formula to solve for cosθ, and then you can use your calculator to find θ.

3. Jun 30, 2011

nukeman

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

Yea, I can figure out how to find θ with a calculator no problem, but getting there is where I have problems.

"Use the identity sin2x + cos2x = 1 to convert the sin2θ term, and then you will have an equation that is quadratic in form, in cosθ. Use the quadratic formula to solve for cosθ"

This is where I run into problems......

4. Jun 30, 2011

Staff: Mentor

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

Which part are you having trouble with?

5. Jun 30, 2011

Staff: Mentor

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

My earlier advice was more general that it needed to be. You don't need to use the quadratic formula to solve the resulting equation. It can be factored pretty easily.

6. Jun 30, 2011

nukeman

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

2 issues. Before I get to the 2 issues, whenever I have this type of question, what is the first thing I look to do?

Having issues with the first step, converting the sin term.... And why am I trying to convert the sin term?

After that, would I factor it?

Thanks, appreciate it!

7. Jun 30, 2011

Staff: Mentor

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

That's hard to say, and a "one size fits all" strategy probably isn't useful. It depends on the problem.
There's no sin term. There is a sin2θ term, though, and you can use the identity I gave earlier to convert to cos2θ. That way, you will have an equation that involves cosθ and cos2θ that will be quadratic in form. Once you get to that point, the equation can be factored.

8. Jun 30, 2011

nukeman

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

So, afters its factored, I can then use my calculator to solve for Theta?

9. Jun 30, 2011

Staff: Mentor

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

Yeah, but you shouldn't need to.

10. Jun 30, 2011

nukeman

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

I shouldnt need a calc?

11. Jun 30, 2011

Staff: Mentor

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

Do you understand what "shouldn't need to" means?

12. Jun 30, 2011

nukeman

Re: Having Trouble: Solving a Trigonometric Equation using Identities ???

Thanks