Radians and Degrees. What the heck is a radian? The radian is a unit of angular measure defined such that an angle of one radian subtended from the center.

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Presentation transcript:

Radians and Degrees

What the heck is a radian? The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1.unit circlearc length Say what now?! Radian: the angle made by taking the radius and wrapping it along the edge of a circle.

Radians as Ratios

Radians and Degrees

Converting: Radians to Degrees

Practice Converting Radians to Degrees

Converting: Degrees to Radians

Practice Converting Degrees to Radians 1.320°1.320° 2.45 °2.45 ° 3.165°3.165° °4.540 °

Common Angles In Radians

The Unit Circle

Measuring Angles: Terms Greek letters are used to name angles. Ex: Alpha ( ) Beta ( ) and Theta ( ) Greek letters are used to name angles. Ex: Alpha ( ) Beta ( ) and Theta ( ) Initial Side – this is the starting position of the angle Initial Side – this is the starting position of the angle Terminal Side – this is the ending position of the angle Terminal Side – this is the ending position of the angle Standard Position – vertex on the origin, initial side on the positive x-axis Standard Position – vertex on the origin, initial side on the positive x-axis

Measuring Angles: Terms Positive Angles – angles that are rotated counterclockwise (CCW) Positive Angles – angles that are rotated counterclockwise (CCW) Negative Angles – angles that are rotated clockwise (CW) Negative Angles – angles that are rotated clockwise (CW) Coterminal Angles – angles that have the same initial and terminal sides Coterminal Angles – angles that have the same initial and terminal sides Coterminal Angles Coterminal Angles Negative Angle Positive Angle Coterminal Angles

Sketching Angles Use the unit circle angles to help you approximate where your angle should be. Use the unit circle angles to help you approximate where your angle should be. Start in standard position. If the angle is positive, move counterclockwise. If the angle is negative, move clockwise. Start in standard position. If the angle is positive, move counterclockwise. If the angle is negative, move clockwise. Use arrows to indicate how many (if any) full revolutions the angle has made Use arrows to indicate how many (if any) full revolutions the angle has made

Finding Coterminal Angles

Quadrants and Quadrantal Angles Quadrant 1Quadrant 2 Quadrant 3 Quadrant 4