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Firstly let's expand out the staring equation getting rid of any brackets. This gives: 2-2cos(x)) = 3sin^2(x). Now we can spot that the sin^2(x) term is in the first equation but no the final one. So let'...

Solution: Parametric Differentiation with utilisation of Chain Rule.
By the chain rule: dy/dx = dy/dt * dt/dx
Note: dt/dx = 1 / (dx/dt)
So dy/dt = 0, dx/dt = 3at^2
So dy/dx = 0 * 1/(3a...

You can solve a cubic by applying factor theorem. This is where you plug different values for x into your cubic f(x) = ax^3 + bx^2 + cx + d such that x is a factor of d, until you find a value t for which...

This question requires integration since the area under the curve is equal to the integral between these bounds. Initially let u=3x-2 and differentiate with respect to x so then du/dx = 3. Rearrange to dx...

First, you have to work out the values of t1 and t2 at which the particle is at rest. This is done by solving the quadratic equation for v, producing values for t of 13/8 +- sqrt(137): 0.1619s and 3.088s....