# Thread: Preparing for next year 5

1. ## Preparing for next year 5

Hi,

I've asked for a list of questions from a teacher to do over the holidays. I'm struggling to use the text book to help me.

Could someone provide HOW to do these questions, as I just want to get an idea of what I'm getting next year.

Thanks.

9. Solve for $0 <= x <= 2pi$
a) $sin2x = cosx$
b) $1+sinx=cos2x$
c) $cos2x=sinx$
d) $cos^2x+2cosxsinx-sin^2x=0$

2. Originally Posted by jonoe
Hi,

I've asked for a list of questions from a teacher to do over the holidays. I'm struggling to use the text book to help me.

Could someone provide HOW to do these questions, as I just want to get an idea of what I'm getting next year.

Thanks.

9. Solve for $0 <= x <= 2pi$
a) $sin2x = cosx$
b) $1+sinx=cos2x$
c) $cos2x=sinx$
d) $cos^2x+2cosxsinx-sin^2x=0$
a) Substitute sin(2x) = 2 sin(x) cos(x), re-arrange, factorsie and use null factor law to get two simple trig equations to solve.

b) Substitute $\cos(2x) = 1 - 2\sin^2(x)$, substitute w = sin(x), re-arrange into a quadratic equation, solve for w and hence get two simple trig equations to solve.

c) See b).

d) Substitute $\cos^2 (x) - \sin^2(x) = \cos(2x)$ and $2 \sin(x) \cos(x) = \sin(2x)$, re-arrange to get $\tan(2x) = -1$ and solve for x.

I strongly advise that you find a textbook that explains this topic and has examples to follow. We cannot tutor you in material you have not been taught. And I don't see that there's any point at all in trying to do questions based on material you have not been taught. Clearly you are expected to review this material prior to attempting the questions.