Find All Solutions of Cos 2 Theta Sin Theta

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Precalculus Mathematics Homework Help

Trig Question: cos(2theta) = sin(theta), solve.

Thread starter nukeman
Start date Sep 22, 2012

Homework Statement

I am trying to work through a trig review I found online, but this is the type of question I am needing to be able to solve. If anyone can be so kind to send me a link to a tutorial on how to solve these, I would REALLY appreciate it. Anyways, on to the question! :)

cos(2theta) = sin(theta), solve.

Homework Equations

The Attempt at a Solution

All I can think of is changing cos2theta so there is no more 2.

? What is the aim of a question like this, or this type of trig questions. ?

Answers and Replies

You want to use trig identities to make both sides equal. Cos(2θ) has another form for example.

Ok right, since we are not allowed to have a list of trig identities, and given this type of question, what are the most important trig indentities I need to memorize?

So this question is basically just asking me to prove the identity that cos2theta = sintheta?

So this question is basically just asking me to prove the identity that cos2theta = sintheta?

Yes.

Ok right, since we are not allowed to have a list of trig identities, and given this type of question, what are the most important trig indentities I need to memorize?
So this question is basically just asking me to prove the identity that cos2theta = sintheta?

No, that is not true, so that is not what the question is asking. It is just asking you to solve an equation involving θ. For some (i.e., most) values of θ the equation will be false, but for some special values it will be true. You can perhaps use the relationship between cos(2θ) and sin(θ) and cos(θ) to re-write the equation in a way that may be easier to deal with.

RGV

1st part:
1) Make the right hand side equal to 90. Note only for sin and cos.
2) solve like a normal equation eg. 2thetha+thetha = 90

2nd part:
1) sin(thetha), second quadrant, would become, sin(180-thetha)
2) Make right hand side equal 90,drop sin cos, solve like a normal equation.

1st part:
1) Make the right hand side equal to 90. Note only for sin and cos.
2) solve like a normal equation eg. 2thetha+thetha = 90
2nd part:
1) sin(thetha), second quadrant, would become, sin(180-thetha)
2) Make right hand side equal 90,drop sin cos, solve like a normal equation.

I have no idea what you are talking about. '1st part' of what? There was only one equation given here. 'Right side' of what? The right side of the only given equation was "sin(theta)" and that is certainly not "90"! Nor is theta.