convert the following common angles from degrees to radians in the diagram below. enter each answer as a…

Explanation:

Step1: Use the conversion formula

The formula to convert degrees to radians is ( \text{Radians}=\frac{\pi}{180}\times\text{Degrees} ).

Step2: Calculate each angle

• For (30^{\circ}): ( \frac{\pi}{180}\times30=\frac{\pi}{6} )
• For (45^{\circ}): ( \frac{\pi}{180}\times45=\frac{\pi}{4} )
• For (60^{\circ}): ( \frac{\pi}{180}\times60=\frac{\pi}{3} )
• For (90^{\circ}): ( \frac{\pi}{180}\times90=\frac{\pi}{2} )
• For (120^{\circ}): ( \frac{\pi}{180}\times120=\frac{2\pi}{3} )
• For (135^{\circ}): ( \frac{\pi}{180}\times135=\frac{3\pi}{4} )
• For (150^{\circ}): ( \frac{\pi}{180}\times150=\frac{5\pi}{6} )
• For (180^{\circ}): ( \frac{\pi}{180}\times180=\pi )
• For (210^{\circ}): ( \frac{\pi}{180}\times210=\frac{7\pi}{6} )
• For (225^{\circ}): ( \frac{\pi}{180}\times225=\frac{5\pi}{4} )
• For (240^{\circ}): ( \frac{\pi}{180}\times240=\frac{4\pi}{3} )
• For (270^{\circ}): ( \frac{\pi}{180}\times270=\frac{3\pi}{2} )
• For (300^{\circ}): ( \frac{\pi}{180}\times300=\frac{5\pi}{3} )
• For (315^{\circ}): ( \frac{\pi}{180}\times315=\frac{7\pi}{4} )
• For (330^{\circ}): ( \frac{\pi}{180}\times330=\frac{11\pi}{6} )
• For (0^{\circ},360^{\circ}): ( \frac{\pi}{180}\times0 = 0) and ( \frac{\pi}{180}\times360 = 2\pi)

Answer:

(0^{\circ},360^{\circ}=0,2\pi); (30^{\circ}=\frac{\pi}{6}); (45^{\circ}=\frac{\pi}{4}); (60^{\circ}=\frac{\pi}{3}); (90^{\circ}=\frac{\pi}{2}); (120^{\circ}=\frac{2\pi}{3}); (135^{\circ}=\frac{3\pi}{4}); (150^{\circ}=\frac{5\pi}{6}); (180^{\circ}=\pi); (210^{\circ}=\frac{7\pi}{6}); (225^{\circ}=\frac{5\pi}{4}); (240^{\circ}=\frac{4\pi}{3}); (270^{\circ}=\frac{3\pi}{2}); (300^{\circ}=\frac{5\pi}{3}); (315^{\circ}=\frac{7\pi}{4}); (330^{\circ}=\frac{11\pi}{6})