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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: KiNSKi01 on November 11, 2017, 02:37:58 pm

Title: Circular Functions Question
Post by: KiNSKi01 on November 11, 2017, 02:37:58 pm: Can someone please help with this question!?

I can get to cosx/sinx - 1/sinx but then I don't know what to do. Any general tips for these sorts of questions involving reciprocal functions and unknown angles? :-\
Title: Re: Circular Functions Question
Post by: Sine on November 11, 2017, 02:41:12 pm: Quote from: KiNSKi01 on November 11, 2017, 02:37:58 pm
Can someone please help with this question!?

I can get to cosx/sinx - 1/sinx but then I don't know what to do. Any general tips for these sorts of questions involving reciprocal functions and unknown angles? :-\
sub in a very random number i.e. 0.1423431 into each of the answers and the question and the one which matches is correct.
Title: Re: Circular Functions Question
Post by: KiNSKi01 on November 11, 2017, 03:26:57 pm: But what do you do when its not multiple choice?
Title: Re: Circular Functions Question
Post by: Willba99 on November 11, 2017, 06:38:54 pm: Quote from: KiNSKi01 on November 11, 2017, 03:26:57 pm
But what do you do when its not multiple choice?
suffer

or type them into cas and ask it to simplify. stranger things have happened
Title: Re: Circular Functions Question
Post by: KiNSKi01 on November 11, 2017, 07:09:44 pm: Quote from: Willba99 on November 11, 2017, 06:38:54 pm
suffer

That's probably what I'm best at in spesh
Title: Re: Circular Functions Question
Post by: jazzycab on November 12, 2017, 02:24:16 pm: $\begin{align*} \cot{\left(2\theta\right)}\left(1-\sec{\left(2\theta\right)}\right)&=\frac{\cos{\left(2\theta\right)}}{\sin{\left(2\theta\right)}}\left(1-\frac{1}{\cos{\left(2\theta\right)}}\right)\\ &=\frac{\cos{\left(2\theta\right)}-1}{\sin{\left(2\theta\right)}}\\ &=\frac{\cos^2{\left(\theta\right)}-\sin^2{\left(\theta\right)}-1}{2\cos{\left(\theta\right)}\sin{\left(\theta\right)}}\\ &=\frac{-\left(1-\cos^2{\left(\theta\right)}\right)-\sin^2{\left(\theta\right)}}{2\cos{\left(\theta\right)}\sin{\left(\theta\right)}}\\ &=\frac{-2\sin^2{\left(\theta\right)}}{2\cos{\left(\theta\right)}\sin{\left(\theta\right)}}\\ &=-\frac{\sin{\left(\theta\right)}}{\cos{\left(\theta\right)}}\\ &=-\tan{\left(\theta\right)} \end{align*}$
Title: Re: Circular Functions Question
Post by: cookiedream on November 12, 2017, 02:45:45 pm: Was going to post my working out but jazzycab was faster than me ahaha

When it comes to trig questions like these, especially where double angle formulae are involved, I usually do it by hand. Particularly because these kind of questions can come up in Exam 1. Probably the best way to tackle these questions is to keep in mind common trends/tricks involved in its working out. These include converting tan(x) to sin(x)/cos(x) (or its reciprocal when it's cot(x)), expanding sin(2x) to be 2sin(x)cos(x), etc.
Title: Re: Circular Functions Question
Post by: KiNSKi01 on November 12, 2017, 04:33:26 pm: Thank you very much jazzycab and cookiedream!

Was finding these questions as well as proofs fairly difficult :P