Question

convert the following common angles from degrees to radians in the diagram below. enter each answer as a reduced fraction involving π in the interval 0,2π.

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, use the formula \( \text{Radians}=\frac{\pi}{180}\times\text{Degrees} \).

Step2: Calculate each angle

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

Answer:

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