Answer:
Ф = 120° and Ф = 240°
Step-by-step explanation:
Temporarily replace cos Ф with x, and solve the resulting quadratic equation for x:
2x^2 - 7x - 4 = 0. This factors as follows: (2x + 1)(x - 4) = 0, and so x = -1/2 and x = 4.
But we let x represent cos Ф. Thus, we need to solve the two equations
x = cos Ф = -1/2 and x = cos Ф = 4. The latter equation has no solution, as -1 ≤ cos Ф ≤ 1.
cos Ф is negative in Quadrants II and III. If in Quadrant II, the adjacent side is -1 and the hypotenuse is 2nd so Ф = arccos -1/2 = 120°. If in Quadrant III, the adjacent side is -1 again and the hypotenuse 2 again, so Ф = 240°.
The exact solutions are Ф = 120° and Ф = 240°.
