Thread: Trig Identities - solve the following for 0 <_ θ <_ 4pi

1. Trig Identities - solve the following for 0 <_ θ <_ 4pi

solve the following for 0 <_ θ <_ 4pi

The <_ represents less than or equal to.

Sin[θ]^2 == -Cos[θ]

Would like a step by step process for approaching this question. Thanks.

2. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

Originally Posted by dcpc10
solve the following for 0 <_ θ <_ 4pi
Sin[θ]^2 == -Cos[θ]

If the question is to solve $\sin^2(\theta)=-\cos(\theta)$ then that is equivalent to solving $\cos^2(\theta)-\cos(\theta)-1=0$.

Or $u^2-u-1=0$ where $u=\cos(\theta).$

If that is not what it means, then please correct it.

3. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

Yes that is what it means.

4. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

So you can solve it now?

5. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

No because I would appreciate a step by step process to solve it. That was the reasoning for making the thread in the first place. This is for gr 12 advanced functions.

6. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

Originally Posted by dcpc10
No because I would appreciate a step by step process to solve it. That was the reasoning for making the thread in the first place. This is for gr 12 advanced functions.

Show us your solution to $u^2-u-1=0$.

8. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

Originally Posted by dcpc10
Go and learn to do middle school algebra.
We are not a tutorial service.

9. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

Very unhelpful, you fail to communicate what requires solving and instead would rather confuse those seeking assistance. This is not a tutoring service obviously but its suppose to be a "math help" forum so it totally defeats the purpose if you are unwilling to help solve the problem at hand. Why would you ask me to solve a question totally unrelated if I do not know how it connects to the end answer? That is not going to help anyone. Geez very disappointing..

10. Re: Trig Identities - solve the following for 0 <_ θ <_ 4pi

Do you know how to solve cos(θ) = k?
Do you know the identity sin^2(θ) + cos^2(θ) == 1?
Can you solve quadratic equations?

These are prerequisites to solving this equation.