Having Trouble: Solving a Trigonometric Equation using Identities ?

[nukeman]

Having Trouble: Solving a Trigonometric Equation using Identities ?

Homework Statement

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 ?

Homework Equations

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

 

[Mark44]

Homework Statement

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 ?

Homework Equations

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

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.

 

[nukeman]

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.

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...

 

[Mark44]

Which part are you having trouble with?

 

[Mark44]

Which part are you having trouble with?

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.

 

[nukeman]

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!

 

[Mark44]

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?

That's hard to say, and a "one size fits all" strategy probably isn't useful. It depends on the problem.

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!

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.

 

[nukeman]

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

 

[Mark44]

Yeah, but you shouldn't need to.

 

[nukeman]

I shouldn't need a calc?

 

[Mark44]

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

Yeah, but you shouldn't need to.

I shouldn't need a calc?

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

 

[nukeman]

Thanks