x = 5 + 6 cos 2t + 8 sin 2t,

where x is the displacement in metres and t is the time in seconds.

(i) Prove that the particle is moving in simple harmonic motion by showing 2

2 that x satisfies an equation of the form x = −n ( x − c).

(ii) When is the displacement of the particle zero for the first time? 3

in questions (ii),

how do you Rewrite 6cos2t + 8sin2t = −5 as 10cos(2t − α) = −5

is there any reason why it becomes cos(2t - a)