UpStudy Free Solution:

To convert \(- \frac { 7\pi } { 4} \) radians to degrees, use the conversion factor that \(\pi \) radians is equivalent to \(180^ \circ \).

1. Set up the conversion:

\[- \frac { 7\pi } { 4} \times \frac { 180^ \circ } { \pi } \]

2. Cancel out \(\pi \):

\[- \frac { 7} { 4} \times 180^ \circ \]

3. Perform the multiplication:

\[- \frac { 7 \times 180^ \circ } { 4} = - \frac { 1260^ \circ } { 4} = - 315^ \circ \]

So, \(- \frac { 7\pi } { 4} \) radians is equivalent to \(- 315^ \circ \).

Supplemental Knowledge

Converting between radians and degrees is a common task in trigonometry. The relationship between radians and degrees is based on the fact that \(\pi \) radians is equal to \(180^ \circ \). This conversion factor allows us to switch between these two units of angular measurement.

Conversion Formula:

- To convert from radians to degrees, use the formula:

\[\text { Degrees} = \text { Radians} \times \frac { 180^ \circ } { \pi } \]

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