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First, you start by replacing sin^2(x) with 1-cos^2(x) as you want the equation to be in terms of cos(x) and you know sin^2(x)+cos^2(x) = 1. Then you rearrange the equation to get 0 on one side so that yo...

It states that for a right-angle triangle, the square of the hypotenuse equals the sum of the squares of the other sides. So if a denotes the hypotenuse, a^2 = b^2 + c^2.

When factorising a quadratic the idea is to separate it into two brackets, so first, I usually write out the empty brackets like this; (x___)(x___) You then need to think of numbers that you can put in th...

x^4 -8x^2 +15 = 0, we rewrite the equation in square form as (x^2-4)^2 -16 +15 =0 (x^2 -4)^2 = 1 x^2 -4 = ±1 so x^2 = 4±1, (x^2 = 3 or x^2 = 5) Therefore x = {-√3, √3, -√5, √5)

In order to find turning points, we differentiate the function. Hence we get f'(x)=2x + 4. Setting f'(x)=0 we get x = -2 and inputting this into f(x) we get y = 0 therefore the turning point is (-2,0). To...