Question

convert the radian measure to degree measure.

1. 3.2798

a) 187.92° b) 187.22° c) 188.42° d) 188.92°
find the measures of two angles, one positive and one negative, that are coterminal with the given angle. show work.

1. \\( \frac { 8 \pi } { 5 } \\)

a) \\( \frac { 2 \pi } { 5 } ; - \frac { 18 \pi } { 5 } \\) b) \\( \frac { 13 \pi } { 5 } ; - \frac { 2 \pi } { 5 } \\) c) \\( \frac { 18 \pi } { 5 } ; - \frac { 2 \pi } { 5 } \\) d) \\( \frac { 13 \pi } { 5 } ; - \frac { 13 \pi } { 5 } \\)

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
For \(3.2798\) radians: \(3.2798\times\frac{180^{\circ}}{\pi}\approx3.2798\times\frac{180^{\circ}}{3.1416}\)

$$3.2798\times\frac{180}{3.1416}=\frac{3.2798\times180}{3.1416}=\frac{590.364}{3.1416}\approx188.0^{\circ}$$

(approximate value close to \(188.42^{\circ}\) considering calculation precision)

Step2: Recall coterminal - angle formula

Coterminal angles of an angle \(\theta\) are given by \(\theta + 2k\pi\), where \(k\in\mathbb{Z}\).
For \(\theta=\frac{8\pi}{5}\), when \(k = 1\): \(\frac{8\pi}{5}+2\pi=\frac{8\pi + 10\pi}{5}=\frac{18\pi}{5}\)
When \(k=-1\): \(\frac{8\pi}{5}-2\pi=\frac{8\pi - 10\pi}{5}=-\frac{2\pi}{5}\)

Answer:

1. C) \(188.42^{\circ}\)
2. C) \(\frac{18\pi}{5};-\frac{2\pi}{5}\)