# Having Trouble: Solving a Trigonometric Equation using Identities ?

• nukeman
In summary, having trouble solving a trigonometric equation using identities? 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. After that, factor the equation.
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 ?

## 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

nukeman said:

## 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 ?

## 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.

Mark44 said:
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...

Which part are you having trouble with?

Mark44 said:
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.

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!

nukeman said:
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.
nukeman said:
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.

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?

nukeman said:
So, afters its factored, I can then use my calculator to solve for Theta?
Mark44 said:
Yeah, but you shouldn't need to.
nukeman said:
I shouldn't need a calc?
Do you understand what "shouldn't need to" means?

Thanks

## 1. What is a trigonometric identity?

A trigonometric identity is an equation that is true for all values of the variables within a specific domain. These identities are used to simplify and manipulate trigonometric expressions and equations.

## 2. How do I know when to use trigonometric identities to solve an equation?

You can use trigonometric identities to solve an equation when the equation involves trigonometric functions, such as sine, cosine, or tangent, and the goal is to simplify or manipulate the equation.

## 3. What are the most commonly used trigonometric identities?

The most commonly used trigonometric identities are the Pythagorean identities, the sum and difference identities, and the double angle identities. These identities are used to simplify and manipulate trigonometric expressions and equations.

## 4. How do I use trigonometric identities to solve an equation?

To solve an equation using trigonometric identities, you must first identify which identity or identities can be used to simplify the equation. Then, you must apply the identity or identities to both sides of the equation, following the rules of algebra to isolate the variable. Finally, you can solve for the variable and check your solution by substituting it back into the original equation.

## 5. Are there any tips for using trigonometric identities to solve equations?

One tip for using trigonometric identities to solve equations is to always check if the equation can be simplified or manipulated using an identity before attempting to solve it using other methods. It is also helpful to have a list of common trigonometric identities and their variations on hand for reference.

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