the function $k$ is given by $k(\theta)=2sin\theta$. what are all values of $\theta$, for $0leq\theta<2pi$…

the function $k$ is given by $k(\theta)=2sin\theta$. what are all values of $\theta$, for $0leq\theta<2pi$, where $k(\theta)= - 1$?\n(a) $\theta=\frac{pi}{6}$ and $\theta=\frac{5pi}{6}$\n(b) $\theta=\frac{pi}{3}$ and $\theta=\frac{5pi}{3}$\n(c) $\theta=\frac{2pi}{3}$ and $\theta=\frac{4pi}{3}$\n(d) $\theta=\frac{7pi}{6}$ and $\theta=\frac{11pi}{6}$

the function $k$ is given by $k(\theta)=2sin\theta$. what are all values of $\theta$, for $0leq\theta<2pi$, where $k(\theta)= - 1$?\n(a) $\theta=\frac{pi}{6}$ and $\theta=\frac{5pi}{6}$\n(b) $\theta=\frac{pi}{3}$ and $\theta=\frac{5pi}{3}$\n(c) $\theta=\frac{2pi}{3}$ and $\theta=\frac{4pi}{3}$\n(d) $\theta=\frac{7pi}{6}$ and $\theta=\frac{11pi}{6}$

Answer

Explanation:

Step1: Set up the equation

Set (k(\theta)=2\sin\theta=- 1), then (\sin\theta =-\frac{1}{2}).

Step2: Recall sine - unit - circle values

We know that on the unit - circle, for (0\leq\theta<2\pi), (\sin\theta = y) - coordinate of the point on the unit - circle corresponding to the angle (\theta). The angles for which (\sin\theta=-\frac{1}{2}) in the given range are (\theta=\frac{7\pi}{6}) and (\theta = \frac{11\pi}{6}).

Answer:

D. (\theta=\frac{7\pi}{6}) and (\theta=\frac{11\pi}{6})