Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\cos \theta = - \frac { 1 } { 2 }$ and $\sin \theta

Question

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\cos \theta = - \frac { 1 } { 2 }$ and $\sin \theta < 0$
A) $\frac { 5 \pi } { 6 }$
B) $\frac { 4 \pi } { 3 }$
C) $\frac { 7 \pi } { 6 }$
D) $\frac { 2 \pi } { 3 }$

Quizplus · Accepted Answer

The cosine of an angle is negative in the second and third quadrants, but since the sine of the angle is also negative, the angle must be in the third quadrant. Among the given options, $\frac { 4 \pi } { 3 }$ is the only angle in the third quadrant where $\cos \theta = - \frac { 1 } { 2 }$.

Find the Value of the Unique Real Number Between 0 cos⁡θ=−12\cos \theta = - \frac { 1 } { 2 }cosθ=−21​

Find the Value of the Unique Real Number Between 0 $\cos \theta = - \frac { 1 } { 2 }$