# Trigonometry Identity problem I been trying to solve all day

• Juliano
In summary, the equation 3 cos(x) + 1 + 2 cos^2(x)=0 can be solved for 0 if the cos(x) and cos^2(x) are both positive.
Juliano

## Homework Statement

solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2pi

## The Attempt at a Solution

3(cos(x) + 1) = 2 sin^2(x)
3(cos(x) + 1) = 2 (1- cos^2(x))
I've tried this variation, and a couple others but it just does not pan out. Please help.

Oh yeah we have a real uninformative book.

Juliano said:
3(cos(x) + 1) = 2 sin^2(x)
3(cos(x) + 1) = 2 (1- cos^2(x))
I've tried this variation, and a couple others but it just does not pan out. Please help.

Oh yeah we have a real uninformative book.
Don't factor out the 3 on the left side. Instead, distribute the right side, and move everything to the left side. After doing that, do you recognize the equation?

01

OK so I get the following
3 cos(x) + 3 = 2 - 2 cos^2(x)
3 cos(x) + 1 + 2 cos^2(x)=0
I tried this variation before, but I was unsure of what to do with the 1+2 cos^2(x) part. or maybe I'm just doing something wrong with the distribution and movement of the right side.

hold on I think I understand now.
(3 cos(x)+1)(2cos^2(x))= 0, the solve those two for 0

No no no, that's not right. It's best if you put the equation in "standard form" first, like this:
2cos^2(x) + 3 cos(x) + 1 = 0
Do you see what to do now?

01

wow. My head was so wrapped up in Identities I didn't even think to factor them in standard form
(cos +1)(2cos+1)=0
Thank you for shining a light through this fogged up brain of mine

Juliano said:
hold on I think I understand now.
(3 cos(x)+1)(2cos^2(x))= 0, the solve those two for 0
Althought the correct approach has already been pointed out, the equation above deserves a further comment. You can't get to the equation above from the one you showed in a previous post:
3 cos(x) + 1 + 2 cos^2(x)=0
If you multiply out your factored form, you get only two terms, not the three shown just above.

Yeah I see what you mean Mark44, Teachers always tell you to double check doing what you just did. Maybe I need to start doing that more.

Yeah, maybe you should, especially when you're in the early stages of learning something.

## 1. What is a trigonometric identity?

A trigonometric identity is an equation that is true for all values of the variables involved. It is used to simplify and solve trigonometric expressions and equations.

## 2. What is the difference between a trigonometric identity and a trigonometric equation?

A trigonometric identity is an equation that is always true, while a trigonometric equation is an equation that is only true for certain values of the variables.

## 3. How do I know which trigonometric identity to use?

Knowing which trigonometric identity to use depends on the form of the expression or equation you are trying to simplify or solve. You can use trigonometric identities such as the Pythagorean identity, double angle identities, or sum and difference identities.

## 4. How can I remember all the trigonometric identities?

One way to remember the trigonometric identities is to practice using them frequently. You can also create flashcards or mnemonic devices to help you remember them. It is also helpful to understand the concepts behind the identities, rather than just memorizing them.

## 5. What are some common mistakes to avoid when solving trigonometric identities?

Some common mistakes to avoid when solving trigonometric identities include not using the correct identity, not simplifying expressions correctly, and forgetting to check for extraneous solutions. It is also important to be familiar with basic algebraic rules and properties when solving trigonometric identities.

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