Question

Solve the equation 8sin^2𝑥−7=2cos𝑥 for 0≤𝑥≤360°, giving your answers to 1 decimal place.

Answer 1

Explanations & Calculations

$\qquad\qquad \begin{aligned} \small 8\sin^2x-7&=\small 2\cos x\\ \small 8(1-\cos^2x)-7&=\small 2\cos x\\ \small 8\cos^2x+2\cos x-1&=\small 0\\ \small (4\cos x-1)(2\cos x+1)&=\small 0\\ \small \cos x &= \small \frac{1}{4}\quad: \, x = 75.5^0\,\&\,284.5^0\\ \small or\\ \small \cos x&=\small -\frac{1}{2}\quad: x=120.0^0\,\&\,240.0^0 \end{aligned}$