Question

a ray centered at the origin and starting at the positive x - axis is rotated counterclockwise, first by an angle of \\( \frac { 3 \pi } { 5 } \\), then by an additional right angle. the resultant ray is coterminal with a ray that starts at the positive x - axis is rotated by what single angle?
choose the option that best answers the question.
\\( 108 ^ { \circ } \\)
\\( 135 ^ { \circ } \\)
\\( 175 ^ { \circ } \\)
\\( 198 ^ { \circ } \\)

Explanation:

Step1: Convert radians to degrees

We know that to convert radians to degrees, we use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
For \(\frac{3\pi}{5}\) radians, \( \frac{3\pi}{5}\times\frac{180^{\circ}}{\pi}= 3\times36^{\circ}=108^{\circ}\).

Step2: Add the right - angle

A right - angle is \(90^{\circ}\).
The total angle of rotation is \(108^{\circ}+90^{\circ}=198^{\circ}\).

Answer:

\(198^{\circ}\)