Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from geometry. What is.

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Presentation transcript:

Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from geometry. What is a Radian? Definition of an Angle: A union of two rays with a common endpoint (vertex). One side remains fixed and the other side rotates to form an angle. The side that remains fixed is called the initial side…

Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from geometry. What is a Radian? Definition of an Angle: A union of two rays with a common endpoint (vertex). One side remains fixed and the other side rotates to form an angle. The side that remains fixed is called the initial side… and the side that rotates is called the terminal side. We often use the Greek letter theta to represent an angle in trigonometry. When the terminal side rotates in a counterclockwise direction the angle has a positive value.

Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from geometry. What is a Radian? Definition of an Angle: A union of two rays with a common endpoint (vertex). One side remains fixed and the other side rotates to form an angle. The side that remains fixed is called the initial side… We often use the Greek letter theta to represent an angle in trigonometry. When the terminal side rotates in a clockwise direction the angle has a negative value. and the side that rotates is called the terminal side.

Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from geometry. What is a Radian? Geometry Review: Given a circle with center A is a central angle is a radius is the circumference is theta’s intercepted arc (Arc Length)

Now that we have our definition established and a refresher of some geometric concepts, we can discover the definition of a radian. Radian:In a circle, a central angle that cuts off an arc equal in length to the radius of the circle has a measure of 1 radian. When s = r we have reached 1 radian The measure of an angle (in radians) is found by dividing the arc length by the radius.

There exists a relationship between degree and radian measurements. Let us now explore that relationship. One full rotation in degrees: One full rotation in radians:

The relationship between degrees and radians results in the following: (Half rotation) These tell me HOW to convert from one unit of measure to the other! (One rotation) Divide by 180 Divide by 

Summary: A radian is a unit of measure for angles. In a circle, a central angle that cuts off an arc equal in length to the radius of the circle has a measure of 1 radian. The measure of an angle (in radians) is found by dividing the arc length by the radius of a circle. To convert from degrees to radians, multiply the degree measure by… To convert from radians to degrees, multiply the radian measure by…