Question

Use the quadratic formula to find all degree solutions and θ if 0° ≤ θ < 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.) cos2 θ + cos θ − 1 = 0 (a) all degree solutions (Let k be any integer.) θ = (b) 0° ≤ θ < 360° θ =

Answer 1

`\theta = 51.8^\circ` or
`\theta = 308.2^\circ`

Explanation:

`\cos^2 \theta + \cos \theta − 1 = 0`

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`\cos \theta = (-1 \pm √(1^2 - 4(1)(-1)))/(2(1))`

`\cos \theta = (-1 \pm √(1 + 4))/(2)`

`\cos \theta = (-1 \pm √(5))/(2)`

`\cos \theta = 0.61803` or
`\cos \theta = -1.61803`

The range of the cos θ function excludes θ = -1.61803, so we discard that solution.

`\theta = 51.8^\circ` or
`\theta = 308.2^\circ`