Question

question #17 convert $\frac{19pi}{4}$ to radians degrees.
855°
1710°
1750°
950°
question #18 determine the angle or angles on the unit - circle that have a cosine ratio of $-\frac{sqrt{3}}{2}$.
θ = 150° and θ = 210°
θ = 120° and θ = 240°
θ = 30° and θ = 330°
θ = 60° and θ = 300°

Explanation:

Step1: Recall conversion formula

To convert radians to degrees, use the formula $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$.

Step2: Substitute the given value

For $\frac{19\pi}{4}$ radians, we have $\text{Degrees}=\frac{19\pi}{4}\times\frac{180^{\circ}}{\pi}$.
The $\pi$ terms cancel out, and $\frac{19}{4}\times180 = 19\times45=855^{\circ}$.

Answer:

1. A. $855^{\circ}$
2. Recall cosine values on unit - circle

The cosine function $y = \cos\theta$ on the unit - circle gives the $x$ - coordinate of the point on the unit - circle corresponding to the angle $\theta$. We know that $\cos150^{\circ}=-\frac{\sqrt{3}}{2}$ and $\cos210^{\circ}=-\frac{\sqrt{3}}{2}$.