ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: fredrick on May 06, 2008, 07:50:20 pm

Title: Disagree with answers
Post by: fredrick on May 06, 2008, 07:50:20 pm: if $cosecx=\frac{-5}{3}, \pi \le x \le \frac{3\pi}{2}$

Find:

a) $sin2x$
b) $cos2x$

My answers are a) $\frac{24}{25}$ and for b) $\frac{7}{25}$

However the solutions say the answers are a) $\frac{-24}{25}$ and for b) $\frac{-7}{25}$ because x is in the 3rd quadrant both sin and cos are negative(WDF its 2x not x but i might b wrong).
Title: Re: Disagree with answers
Post by: Neobeo on May 06, 2008, 08:15:35 pm: Your answers are correct. They have to be positive.
Title: Re: Disagree with answers
Post by: fredrick on May 06, 2008, 08:17:43 pm: thankyou
Title: Re: Disagree with answers
Post by: Collin Li on May 06, 2008, 08:18:43 pm: $\sin x = -\frac{3}{5}$

$\cos 2x = 1 - 2\sin^2x = 1 - \frac{18}{25} = \frac{7}{25}$

I agree with this one.

Now, since $2\pi \leq 2x \leq 3\pi$ , then $2x$ is in quadrant 1 or 2. However, $\cos 2x > 0$ , $2x$ must be in quadrant 1. Hence, $\sin 2x > 0$ and I agree with the other one too. (I'm just verifying things without actually doing the question)