Definition y Radian: The length of the arc above the angle divided by the radius of the circle. x in radians ,

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Presentation transcript:

Definition y Radian: The length of the arc above the angle divided by the radius of the circle. x in radians ,

Definition y x Unit Circle: the circle with radius of 1 unit 1 If r=1, =s in radians ,

Definition The radian measure of an angle is the distance traveled around the unit circle. Since circumference of a circle is 2 r and r=1, the distance around the unit circle is 2

Important Idea If a circle contains 360° or 2 radians, how many radians are in 180° Use to change rads to degrees 180° rads Use to change degrees to rads rads 180°

Try This Change 240° to radian measure in terms of .

Try This Change radians to degree measure. 157.5°

Try This Change radians to degree measure. 171.89°

Definition y x Terminal Side Vertex A Angle A is in standard position Initial Side

Definition If the terminal side moves counter-clockwise, angle A is positive y A x

Definition If the terminal side moves counter-clockwise, angle A is positive y A x

Definition If the terminal side moves counter-clockwise, angle A is positive y x A

Definition If the terminal side moves clockwise, angle A is negative y x A

Definition If the terminal side moves clockwise, angle A is negative y x A

Definition If the terminal side moves clockwise, angle A is negative y x A

Definition If the terminal side moves clockwise, angle A is negative x y A

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Definition y If the terminal side is on an axis, angle A is a quadrantel angle A x

Definition The quadrantal angles in radians

Definition The quadrantal angles in radians

Definition The quadrantal angles in radians

Definition The quadrantal angles in radians The terminal side is on an axis.

Definition Coterminal Angles: Angles that have the same terminal side.

Important Idea To find coterminal angles, simply add or subtract either 360° or 2 radians to the given angle or any angle that is already coterminal to the given angle.

30° x y Analysis 30° and 390° have the same terminal side, therefore, the angles are coterminal y 390° x

30° x y Analysis 30° and 750° have the same terminal side, therefore, the angles are coterminal x y 750°

30° x y Analysis 30° and 1110° have the same terminal side, therefore, the angles are coterminal x y 1110°

30° x y Analysis 30° and -330° have the same terminal side, therefore, the angles are coterminal x y -330°

Try This Find 3 angles coterminal with 60° 420°,780° and -300°

Try This Find two positive angle and one negative angle coterminal with radians. and ,