The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

More FP3 related woes...

Show that sin5θ=16sin5θ−20sin3θ+5sinθ sin 5\theta = 16sin^5 \theta - 20sin^3 \theta + 5sin\theta
Hence show thatsinπ30 sin \frac{\pi}{30} is a root of the equation 32x5−40x3+10x−1=0 32x^5 -40x^3 +10x -1 = 0

The first bit I'm absolutely fine with, just the hence bit is doing my head in, so to speak! I've realised that the second bit is the same as 2(sin5θ)−1 2(sin5\theta) - 1 but I'm really not sure where to go from here or how to show that sinπ30 sin \frac{\pi}{30} is a root.
Any help would be greatly appreciated!
Reply 1
Avatar for SimonM
SimonM
18
Well, one root of 2x−1=02x-1=0 is x=sin⁡π6x = \sin \frac{\pi}{6}
Set 2(...)-1 equal to zero and solve.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you