Solve the equation on the interval $0 \leq \theta

Name: Solve the equation on the interval $0 \leq \theta < 2 \pi .$ -$\cos ^ { 2 } \theta + 2 \cos \theta + 1 = 0$ A) $2 \pi$ B) $\pi$ C) $\frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$ D) $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
Brand: Quizplus
Rating: 4.9 (42 reviews)

Question

Solve the equation on the interval $0 \leq \theta < 2 \pi .$
-$\cos ^ { 2 } \theta + 2 \cos \theta + 1 = 0$
A) $2 \pi$
B) $\pi$
C) $\frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$
D) $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$

Quizplus · Accepted Answer

The given equation is a quadratic in terms of $\cos \theta$. Factoring, we get $(\cos \theta + 1)^2 = 0$, which implies $\cos \theta = -1$. This occurs at $\theta = \pi$ within the given interval.

Solve the Equation on the Interval 0≤θ<2π.0 \leq \theta < 2 \pi .0≤θ<2π.

Solve the Equation on the Interval $0 \leq \theta < 2 \pi .$