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

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.

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. ?

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.

Ray Vickson
Homework Helper
Dearly Missed
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.

HallsofIvy