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Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +......

To begin, we must first use the fact that turning points of a graph occur at points where the gradient is equal to zero, in other words, points where dy/dx =0. Differentiating the equation with and settin...

From the equation x²+y²-8x+10y+41=0, we can find the centre of the circle by the middle two terms -8x+10y and multiplying them by -1/2. So the coordinates of the circle centre are (4...

In order to do that, and this only works for right angled triangles, is using the sine, cosine, and tangent rules. An easy way to remember this is by using the acronym SOH, CAH, TOA that my teacher taught...

The question is asking us to find the value of x. First, we need to multiply the brackets out. To do this, multiply everything in the bracket by 4 so 43x=12x and 4-2=-8 this gives the equation 12...