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60 Degrees to Radians: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">60 Degrees to Radians60 Degrees to Radians: Definition and ExamplesTable of ContentsConverting 60 Degrees to Radians Definition of Degrees and Radians

Degrees and radians are the two primary units used to measure angles. A degree (denoted by °) represents the amount of rotation from the initial arm to the terminal arm, with a complete circle measuring 360°360°360°. When we divide a circle into 360360360 equal parts, each part equals 1 degree.

A radian is defined as the angle subtended at the center of a circle that corresponds to an arc length equal to the radius of the circle. When the arc length equals the radius, the angle is 111 radian. A complete circle represents 2π2\pi2π radians, which means 360∘=2π360^\circ = 2\pi360∘=2π radians. Some common conversions include: 180∘=π180^\circ = \pi180∘=π radians, 90∘=π290^\circ = \frac{\pi}{2}90∘=2π​ radians, and 60∘=π360^\circ = \frac{\pi}{3}60∘=3π​ radians.

Examples of Converting Degrees to Radians Example 1: Converting 60 Degrees to Radians Problem:

Convert 606060 degrees to radians.

Step-by-step solution:

Step 1, Recall the conversion formula. To convert degrees to radians, we multiply the angle in degrees by π180∘\frac{\pi}{180^\circ}180∘π​.

Step 2, Substitute the given angle (60°60°60°) into the formula.

Angle in radians =60∘×π180∘= 60^\circ \times \frac{\pi}{180^\circ}=60∘×180∘π​

Step 3, Simplify the expression.

Angle in radians =60∘×π180∘=60π180=π3= 60^\circ \times \frac{\pi}{180^\circ} = \frac{60\pi}{180} = \frac{\pi}{3}=60∘×180∘π​=18060π​=3π​

Step 4, State the final answer. 606060 degrees is equal to π3\frac{\pi}{3}3π​ radians.

Example 2: Converting 90 Degrees to Radians Problem:

Convert 909090 degrees to radians.

Step-by-step solution:

Step 1, Use the conversion formula to change degrees to radians.

Angle in radians =Angle in degrees×π180∘= \text{Angle in degrees} \times \frac{\pi}{180^\circ}=Angle in degrees×180∘π​

Step 2, Put in the value 90°90°90° for the angle in degrees.

Angle in radians =90∘×π180∘= 90^\circ \times \frac{\pi}{180^\circ}=90∘×180∘π​

Step 3, Simplify the fraction. Angle in radians =90∘×π180∘=90π180=π2= 90^\circ \times \frac{\pi}{180^\circ} = \frac{90\pi}{180} = \frac{\pi}{2}=90∘×180∘π​=18090π​=2π​

Step 4, Write the final answer. 909090 degrees equals π2\frac{\pi}{2}2π​ radians.

Example 3: Converting 200 Degrees to Radians Problem:

Convert 200200200 degrees into radians.

Step-by-step solution:

Step 1, Apply the degrees to radians conversion formula.

Angle in radians =Angle in degrees×π180∘= \text{Angle in degrees} \times \frac{\pi}{180^\circ}=Angle in degrees×180∘π​

Step 2, Fill in 200°200°200° as the angle in degrees.

Angle in radians =200∘×π180∘= 200^\circ \times \frac{\pi}{180^\circ}=200∘×180∘π​

Step 3, Work through the calculation step-by-step.

Angle in radians =200∘×π180∘=200π180= 200^\circ \times \frac{\pi}{180^\circ} = \frac{200\pi}{180}=200∘×180∘π​=180200π​

Step 4, Simplify the fraction by dividing both numerator and denominator by their greatest common factor.

Angle in radians =200π180=20π18=10π9= \frac{200\pi}{180} = \frac{20\pi}{18} = \frac{10\pi}{9}=180200π​=1820π​=910π​

Step 5, State your answer. 200200200 degrees is equal to 10π9\frac{10\pi}{9}910π​ radians.

Comments(2)CCounselorTaraNovember 4, 2025This page on 60 degrees to radians is great! It helped my students grasp the concept easily. Thanks for the clear explanations!

LLawyerDavidNovember 4, 2025This page on 60 degrees to radians was a great help! It made explaining the concept to my students so much easier. Thanks!

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