1 - 4 cos θ = -2 cos^2 θ ; solve the equation for θ, if θ is between 0 and 360 degrees

Question

Question: 1 - 4 cos θ = -2 cos^2 θ

The answers is apparently:

θ=73 deg, 287 deg.

Answer 1

Trigonometric equations:

1) 1-4cosθ = -2 cos^2 (θ)

2) Rearranging the equation in the form of : ax^2 +bx +c=0. quadratic form.

3) 2cos^2(θ) -4cos(θ)+1=0.

40 factoring 2cos^2(θ) -4cos(θ) +1=0. (2cos. -1 ) (cos (θ) +1 ) =0 We cannot factor this expression in a traditional way, so we need to use the quadratic formula or graphing calculator it they allow you to use it to find the answers. keep in mind that your calculator must be in degree by pressing mode then change from radian to degree.

5) I graphed the function, then using the SECOND-TRACE Item #5 I found the intersection of values of θ.

θ=0.292893322 the second intersection was θ=1.7071068 which is greater than 1 and we cannot find the value because the range of the cosine is -1 and 1.

6) Let find the first angle. using graphing calculator; 2ND COS (0.29289322)≈ 73°, the second angle apparently they found by using co-terminal angle by subtracting 360°-73°=287º.

Note to check your answer : cos (73°)=0.2923717047

cos(287°) =0.2923717047