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Trigonometry question

Solve the equation 2sin^2theta = costheta + 2 for values between 0 and 360 degrees.

So the identities are:

sin^2theta + cos^2theta

tantheta=sintheta/costheta


Any help as to how this can be solved would be very much appreciated, thanks :smile:
And sorry for the lack of the use of latex!

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You are having problems as part of your first identity is missing. This is the one you want to use.
Original post by x-Sophie-x
Solve the equation 2sin^2theta = costheta + 2 for values between 0 and 360 degrees.

So the identities are:

sin^2theta + cos^2theta

tantheta=sintheta/costheta


Any help as to how this can be solved would be very much appreciated, thanks :smile:
And sorry for the lack of the use of latex!


You want a quadratic in cos

sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1
(edited 11 years ago)
You're both analogous to Speedy Gonzales :frown:
Reply 4
Original post by Indeterminate
You want a quadratic in cos

sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1


What do you mean by that?

So far I've got:

2(1-cos^2theta)=costheta +2
2-2cos^2theta=costheta +2
-2cos^2theta=costheta

Where do I go after that?
Reply 5
Original post by Felix Felicis
You're both analogous to Speedy Gonzales :frown:


I'm sorry, but what?
Original post by x-Sophie-x
What do you mean by that?

So far I've got:

2(1-cos^2theta)=costheta +2
2-2cos^2theta=costheta +2
-2cos^2theta=costheta

Where do I go after that?


Get everything on one side and factorise :smile:
Original post by x-Sophie-x
I'm sorry, but what?

Nevermind, I was referring to Indeterminate and Mr M xD In response to your last question, you have a quadratic in costheta, solve how you normally would :smile:
Original post by x-Sophie-x
I'm sorry, but what?


He means that we were too quick (comparison to speedy gonzales) :smile:
Reply 9
Original post by Felix Felicis
Nevermind, I was referring to Indeterminate and Mr M xD In response to your last question, you have a quadratic in costheta, solve how you normally would :smile:


Oh I see.

And I have no idea what you mean by that.

costheta +2cos^2theta=0
costheta(1+2costheta)=0

But how would that help me in any way?
Reply 10
Original post by Indeterminate
He means that we were too quick (comparison to speedy gonzales) :smile:


Ah right.
Original post by x-Sophie-x
Oh I see.

And I have no idea what you mean by that.

costheta +2cos^2theta=0
costheta(1+2costheta)=0

But how would that help me in any way?


ab = 0 means a = 0 or b = 0

Arriba! Arriba!
Original post by x-Sophie-x
Oh I see.

And I have no idea what you mean by that.

costheta +2cos^2theta=0
costheta(1+2costheta)=0

But how would that help me in any way?

You have cosθ(1+2cosθ)=0cosθ=0\cos \theta (1 + 2 \cos \theta ) = 0 \Rightarrow \cos \theta = 0 or cosθ=12\cos \theta = -\frac{1}{2} :smile:
^^beat me to it :tongue:
Original post by Mr M
ab = 0 means a = 0 or b = 0

Arriba! Arriba!

And again! xD
(edited 11 years ago)
Reply 15
Original post by Felix Felicis
And again! xD


I see what you meant by MrM now, I hadn't a clue who he was.
Original post by x-Sophie-x
I see what you meant by MrM now, I hadn't a clue who he was.


My fame precedes me.

:frown:
Reply 17
Original post by Felix Felicis
You have cosθ(1+2cosθ)=0cosθ=0\cos \theta (1 + 2 \cos \theta ) = 0 \Rightarrow \cos \theta = 0 or cosθ=12\cos \theta = -\frac{1}{2} :smile:


Oh yeah. Funny how I didn't see that, thanks :smile:

It's annoying how you know the answer to every maths question though :P
Reply 18
Original post by Mr M
My fame precedes me.

:frown:


Haha. Sorry :tongue:
Original post by x-Sophie-x
Oh yeah. Funny how I didn't see that, thanks :smile:

It's annoying how you know the answer to every maths question though :P

:smug: Jelly? :wink:

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