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C3 Basic Trig

tan2θcosec2θ
Simplify
I did tan2θ * 1/sin2θ = tan2θ/sin2θ
However, it is either wrong or i have not simplified far enough?

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is that tan2feta, or tan squared feta?
Reply 2
Original post by DeGoldenGamer
is that tan2feta, or tan squared feta?


tan 2 feta
Reply 3
Original post by DeGoldenGamer
is that tan2feta, or tan squared feta?


Big man what's feta? Lmao, You making me hungry.
Reply 4
Original post by Desultory
tan2θcosec2θ
Simplify
I did tan2θ * 1/sin2θ = tan2θ/sin2θ
However, it is either wrong or i have not simplified far enough?


You didn't really simplify it, you just changed the cosec to a sin

Given these are both functions of 2θ2\theta, you may be expected to use the double angle formulae to change these into expressions of just sinθ\sin\theta and cosθ\cos\theta

Give that a go and let us know what you come up with
Reply 5
Original post by Ed5
You didn't really simplify it, you just changed the cosec to a sin

Given these are both functions of 2θ2\theta, you may be expected to use the double angle formulae to change these into expressions of just sinθ\sin\theta and cosθ\cos\theta

Give that a go and let us know what you come up with


This is c3 year 13 maths? Sorry i dont know the double angle formulae
Reply 6
Original post by Desultory
This is c3 year 13 maths? Sorry i dont know the double angle formulae


If you're on edexcel, aye it's C3 and these formulae are a key part of it. They let you break down trignometric functions into more basic ones, e.g. sin(a+b)=sinacosb+sinbcosa\sin(a+b)=\sin a\cos b + \sin b \cos a

You should definitely cover it in class at some point so it's likely you just haven't reached the topic yet
Reply 7
Original post by Desultory
tan2θcosec2θ
Simplify
I did tan2θ * 1/sin2θ = tan2θ/sin2θ
However, it is either wrong or i have not simplified far enough?

Write tan2θ=sin2θcos2θ\displaystyle \tan 2\theta = \frac{\sin 2\theta}{\cos 2\theta} and see what you notice.

You don't need to use double angle formulae for this question.
Reply 8
Original post by Ed5
If you're on edexcel, aye it's C3 and these formulae are a key part of it. They let you break down trignometric functions into more basic ones, e.g. sin(a+b)=sinacosb+sinbcosa\sin(a+b)=\sin a\cos b + \sin b \cos a

You should definitely cover it in class at some point so it's likely you just haven't reached the topic yet


That is true but this is a section 6 question which is basic trig not section 7 which is further trig so i am not expexted to use that so i need another way?
Reply 9
Original post by Notnek
Write tan2θ=sin2θcos2θ\displaystyle \tan 2\theta = \frac{\sin 2\theta}{\cos 2\theta} and see what you notice.

You don't need to use double angle formulae for this question.


i know tan theta = sin theta / cos theta but if its tan 2 theta, are you allowed to put a 2 infront of the sin and cos theta?
I didnt know that?
Reply 10
Original post by Desultory
i know tan theta = sin theta / cos theta but if its tan 2 theta, are you allowed to put a 2 infront of the sin and cos theta?
I didnt know that?

Yes, the identity is tanAsinAcosA\displaystyle \tan A \equiv \frac{\sin A}{\cos A} , cosA0  , \ \cos A \neq 0 \ \ and since it's an identity, it's true for all AA so you can replace AA with anything.

E.g. tan22=sin22cos22\displaystyle \tan 22 = \frac{\sin 22}{\cos 22}

or tan2θ=sin2θcos2θ\displaystyle \tan 2\theta = \frac{\sin 2\theta}{\cos 2\theta}
(edited 6 years ago)
Reply 11
Original post by Desultory
That is true but this is a section 6 question which is basic trig not section 7 which is further trig so i am not expexted to use that so i need another way?


Original post by Notnek
Write tan2θ=sin2θcos2θ\displaystyle \tan 2\theta = \frac{\sin 2\theta}{\cos 2\theta} and see what you notice.

You don't need to use double angle formulae for this question.


Must just be like this then. I wasn't really sure given you didn't mention the module, and 'simplify' can be quite open ended
Reply 12
Original post by Notnek
Yes, the identity is tanAsinAcosA\displaystyle \tan A \equiv \frac{\sin A}{\cos A} (cosA0\cos A \neq 0) and since it's an identity, it's true for all AA so you can replace AA with anything.

E.g. tan22=sin22cos22\displaystyle \tan 22 = \frac{\sin 22}{\cos 22}

or tan2θ=sin2θcosθ\displaystyle \tan 2\theta = \frac{\sin 2\theta}{\cos \theta}


Okay that makes sense thanks i worked it out now :smile:
However, if there is a question where its tan^2 theta, can that equal sin^2 theta / cos ^2 theta or not?
Reply 13
Original post by Ed5
Must just be like this then. I wasn't really sure given you didn't mention the module, and 'simplify' can be quite open ended


Thankyou for the advice anyway! It made me read ahead and did help :smile:
I appreciated the advice!
Reply 14
Original post by Desultory
Okay that makes sense thanks i worked it out now :smile:
However, if there is a question where its tan^2 theta, can that equal sin^2 theta / cos ^2 theta or not?

Yes that's also true but for a different reason:

tan2θ=(tanθ)2=(sinθcosθ)2=sin2θcos2θ\displaystyle \tan^2 \theta = \left(\tan \theta\right)^2 = \left(\frac{\sin \theta}{\cos \theta}\right)^2 = \frac{\sin^2 \theta}{\cos^2 \theta}
Reply 15
Original post by Notnek
Yes that's also true but for a different reason:

tan2θ=(tanθ)2=(sinθcosθ)2=sin2θcos2θ\displaystyle \tan^2 \theta = \left(\tan \theta\right)^2 = \left(\frac{\sin \theta}{\cos \theta}\right)^2 = \frac{\sin^2 \theta}{\cos^2 \theta}


Okay thanks now these questions seem easy!
Reply 16
Original post by Desultory
Okay thanks now these questions seem easy!

Getting good at C3/4 trigonometry is all about practice. Some students think they can get by if they just learn the identities but this doesn't work. You have to try as many different questions as you can to see how/where identities can be used and to pick up all the little tricks.

When a student tells me that they hate C3 trig (common), I know that they probably haven't practiced enough :smile:
(edited 6 years ago)
Reply 17
Original post by Notnek
Getting good at C3/4 trigonometry is all about practice. Some students think they can get by if they just learn the identities but this doesn't work. You have to try as many different questions as you can to see how/where identities can be used and to pick up all the little tricks.

When a student tells me that they hate C3 trig (common), I know that they probably haven't practiced enough :smile:


haha i completely understand
are you a teacher of maths?
reccommend any good websites for tutors or even yourself?
Reply 18
Original post by Desultory
haha i completely understand
are you a teacher of maths?
reccommend any good websites for tutors or even yourself?

Yes I teach/tutor. If you google "maths tutor" then you'll find websites where you can find tutors near you.
Reply 19
Original post by Notnek
Yes I teach/tutor. If you google "maths tutor" then you'll find websites where you can find tutors near you.

ok thanks

sec A - sec A * sin^2 A

i did 1/cos A - 1/cos A * 1-cos^2A) but it doesnt really simplify
have i done this wrong?

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