What is the degree measure of an angle of \(\frac{7\pi}{4}\) radians?
315°
Radians and degrees are two units for the same angle, linked by the fact that a straight angle is \(\pi\) radians and also 180°.
So to change radians into degrees we multiply by the conversion factor \(\dfrac{180^\circ}{\pi}\).
Here the angle is \(\dfrac{7\pi}{4}\) radians, giving \(\dfrac{7\pi}{4}\times \dfrac{180}{\pi}\).
The \(\pi\) in numerator and denominator cancels, leaving \(\dfrac{7\times 180}{4}\).
Compute the top: \(7\times 180 = 1260\).
Dividing, \(\dfrac{1260}{4} = 315\).
The key concept is the single bridge relation \(\pi \text{ rad} = 180^\circ\), from which every radian-degree conversion follows.
The angle measures 315°.
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