Solve the equation (x in radians and in degrees) for all exact solutions where appropriate. Round approximate answers
in radians to four decimal places and approximate answers in degrees to the nearest tenth.
-$$\cos ^ { 2 } x + 2 \cos x = - 1$$
A) $\{ \pi + 2 n \pi \}$
B) $\{ 2 n \pi \}$
C) $\left\{ \frac { \pi } { 2 } + n \pi , 2 n \pi \right\}$
D) $\{ n \pi \}$

Question

Quizplus · Accepted Answer

This equation can be rearranged into a quadratic form by setting $\cos x = y$, leading to $y^2 + 2y + 1 = 0$, which simplifies to $(y + 1)^2 = 0$. This gives $y = -1$, or $\cos x = -1$. The cosine function equals -1 at $x = \pi + 2n\pi$, where $n$ is any integer, matching option A.

Solve the Equation (X in Radians and in Degrees) for All