4.1 Radian and Degree Measure. Objective To use degree and radian measure.

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Presentation transcript:

4.1 Radian and Degree Measure

Objective To use degree and radian measure.

Angles An angle is determined by rotating a ray about its endpoint. The starting point of the ray is the initial side. The ending position is the terminal side.

Angles The endpoint of the ray is called the vertex of the angle. An angle in standard position has its initial side on the positive x-axis and its vertex at the origin.

Angles If the rotation of the ray is counterclockwise the angle has positive measure. If the rotation of the ray is clockwise the angle has negative measure.

Angles An angle in standard position is said to lie in the quadrant in which its terminal side lies. A central angle of a circle is an angle whose vertex is on the center of the circle.

Degree Measure An angle generated by one complete counterclockwise rotation measures 360°. One generated by a complete clockwise rotation measures -360°.

Coterminal angles Angles that have the same initial and terminal sides are called coterminal.

Radian Measure The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.

Definition of a Radian One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. Algebraically this means that θ = s / r where θ is measured in radians. Radian Demo gonometryRealms/radianDemo1 /RadianDemo1.html gonometryRealms/radianDemo1 /RadianDemo1.html

The circumference of a circle is 2πr. There are 2π radians around the circumference of a circle. There are about 6.28 radians in a full circle.

1 radians = 57.29° 1 degree = radians

To convert degrees to radians: To convert radians to degrees

When no units of angle measure are specified, radian measure is implied.

Example Converting from Degrees to Radians 135°3π/4 540°3π -270°-3π/2

Example Converting from Radians to Degrees