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We must first use the identity cosecθ = 1/sinθ. Now the equation becomes (1/sinθ)(3 cos 2θ+7)+11=0. Since we know that the question is asking for the answer in the form of asin²θ + bsinθ + c = ...

So let's start with taking the natural log on both sides of y=a^x, giving us ln(y) = ln(a^x). Using the laws of logarithms we can write this as ln(y) = xln(a).Next, we differentiate bo...

1. Stationary points occur when dy/dx=0, therefore determine dy/dx first:
   dy/dx= 2x² + 4x - 6
   2) solve dy/dx=0 for two values of x (using quadratic formula, if necessary):
   (x+...

For a question like this you should aim to eliminate either x OR y from one equation in order to deduce the value of the other. 1) 2x +5y + 5= 0 , 2) 2y + 31= 5x
Rearrange equation 2) so that 2y +31...

We firstly need to find the slope of the line normal to the curve at the point (c, lnc). To do this, we will differentiate implicitly the equation of the curve to find the slope of the tangent. By implici...