Answer:
[tex] \theta = 51.8^\circ [/tex] or [tex] \theta = 308.2^\circ [/tex]
Step-by-step explanation:
[tex] \cos^2 \theta + \cos \theta − 1 = 0 [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] \cos \theta = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)} [/tex]
[tex] \cos \theta = \dfrac{-1 \pm \sqrt{1 + 4}}{2} [/tex]
[tex] \cos \theta = \dfrac{-1 \pm \sqrt{5}}{2} [/tex]
[tex] \cos \theta = 0.61803 [/tex] or [tex] \cos \theta = -1.61803 [/tex]
The range of the cos θ function excludes θ = -1.61803, so we discard that solution.
[tex] \theta = 51.8^\circ [/tex] or [tex] \theta = 308.2^\circ [/tex]
