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:
\[\text { Degrees} = \text { Radians} \times \frac { 180^ \circ } { \pi } \]
Make trigonometry accessible with UpStudy! Whether you need help converting angles between radians and degrees or solving more challenging problems, UpStudy's AI Homework Help app delivers accurate solutions immediately with step-by-step explanations to make learning easy! Plus, our elite tutors are online around-the-clock should you require any personalized assistance or simply require personalized help when learning any difficult concept easily! Join millions of other learners worldwide who trust UpStudy as an academic success tool because mastering trigonometry starts by understanding its fundamental principles!