Use the quadratic formula to find all degree solutions and $\theta$ if
$0° \le \theta < 360°$.
Use a calculator to approximate all answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
$$\cos^2 \theta + \cos \theta − 1 = 0$$
(a) all degree solutions (Let $k$ be any integer)
(b) $0° \le \theta < 360°$.
My work so far: http://i.imgur.com/IIlP2eA.jpg
Any help on how I should do this is greatly appreciated…
Best Answer
You know that $$\cos \theta = \frac{-1 - \sqrt{5}}{2} \vee \cos \theta = \frac{-1 + \sqrt{5}}{2}$$.
Only the latter one gives two solutions: $$\theta = 51.8^\circ \vee \theta = 360^\circ - 51.8^\circ = 308.2^\circ$$