Search over 10,000 free study notes

From the following identity, cos(a-b) = cosacosb+ sinasinb, we find that 4sinx+3cosx = R(cosxcosa+sinxsina). We now equate the coefficients: 3 = Rcosa and 4=Rsina. Using basic trigonometry, we can make th...

Firstly square both sides. This way, we now know that both sides have to be positive

(3x+1)^2 = 1

(3x+1)(3x+1) = 1

Expand the quadratic...

9x^2 + 12x + 4 = 1

9x^2 + 12x ...

So we are meant to rearrange the given equation in a way that it looks like: (x+p)^2 + q This should look familiar. It is obtained by completing the square. Which will be the method I will describe below:...

To differentiate a simple expression such as x^3 + 2x you simply multiply the power of the x by the multiple in front of the x value and then take away one from the power. For example the expression would...

so lets deal with 2 first. We can express 2 in terms of log5 by the laws of logs. nlogx=logx^n. re-writing 2 as 2log5=log25 we now have log(x+1)+log5=log25. lets apply a different log law: log(a)-log(b)=l...