Question

How is the radian measure of an angle determined?

Short answer

Answer: To convert a 60-degree angle to radians, we can follow the given steps: Step 1: Write down the given angle measure in degrees (60°). Step 2: Multiply the degree measure by the conversion factor (𝜋/180): 60° * (𝜋/180) = 60𝜋/180 = 𝜋/3 Therefore, the radian measure of a 60-degree angle is 𝜋/3 radians.

Step-by-step solution

Definition of Radian Measure

A radian measure of an angle is the length of the arc on a circle with the radius equal to the radius of the circle. It is a unit of angle measure, used mainly in trigonometry and geometry. In a circle with a radius of 1 unit (known as a unit circle), one radian is defined as the angle subtended at the center of the circle by an arc with a length equal to the radius of the circle.

Relation between Degrees and Radians

There is a relation between degrees and radians which helps us to convert one unit into the another. It should be known that a full circle (360 degrees) is equal to 2𝜋 radians (where 𝜋 is a mathematical constant, approximately 3.14). Based on this fact, we can express the relation between the two units as follows: 1 radian = (180/𝜋) degrees 1 degree = (𝜋/180) radians

Converting Angle from Degrees to Radians

To determine the radian measure of an angle, you need to follow these two steps: Step 1: Write down the given angle measure in degrees. Step 2: Multiply the degree measure by the conversion factor (𝜋/180), which will give you the radian measure of the angle. For example, let's convert a 45-degree angle to radians: 45° * (𝜋/180) = 45𝜋/180 = 𝜋/4 So, the radian measure of a 45-degree angle is 𝜋/4 radians.