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From the addition formula, we know that:

Rcos(x-c) = Rcos(x)sin(c)+Rsin(x)cos(c)

Therefore:

acos(x)+bsin(x) = Rcos(x)cos(c)+Rsin(x)sin(c)

If we e...

If you were to draw a graph of the function, a stationary point would be a point on the graph where the gradient is zero, i.e the graph has no vertical slope. For example consider the function f(x) = 2. T...

To differentiate this, we must use the Chain Rule. This is because we have two functions multiplied by each other:

(x) sin⁡(x).

We use the substitution u = sin(x)....

The first thing to remember is that the tangent to the curve at a given point has the same gradient as the curve at that point.

Let's consider the general case y=f(x) at a point c=(x1,y1)...

Firstly, note that cos^2(x)+5sin^2(x)= cos^2(x) +sin^2(x) +4sin^2(x).

By trignoemtric identies, cos^2(x)+sin^2(x)=1 and so we can just integrate 1+4sin^2(x) since this is equal to cos^2(x...