Question

A question on my test:

Solve each equation over the interval [0°, 360°). If a decimal approximation is necessary, round to four decimal places. cos 2x -cos x-2 = 0

Answer 1

180degrees

Explanation:

Given the expression cos^2x - cos x - 2 = 0

Let P = cos x

P^2 - P - 2 = 0

Factorize

P^2 - 2P + P - 2 =0

P(P-2)+1(P-2) = 0

P-2 = 0 and P + 1 = 0

P = 2 and P = -1

Since P = cos x

cos x = -1

x = arccos(-1)

x = 180degrees

Hence the require angle is 180degrees