# Angles of Rotation and Radian Measure In the last section, we looked at angles that were acute. In this section, we will look at angles of rotation whose.

## Presentation on theme: "Angles of Rotation and Radian Measure In the last section, we looked at angles that were acute. In this section, we will look at angles of rotation whose."— Presentation transcript:

Angles of Rotation and Radian Measure In the last section, we looked at angles that were acute. In this section, we will look at angles of rotation whose measure can be any real number. An angle of rotation is formed by two rays with a common endpoint (called the vertex). initial side terminal side vertex One ray is called the initial side. The other ray is called the terminal side. x y

Angles of Rotation and Radian Measure initial side terminal side vertex x y The measure of the angle is determined by the amount and direction of rotation from the initial side to the terminal side. The angle measure is positive if the rotation is counterclockwise, and negative if the rotation is clockwise. A full revolution (counterclockwise) corresponds to 360º.

Angles of Rotation and Radian Measure x y This is a positive (counter- clockwise) angle y x This is a negative (clockwise) angle

Angles of Rotation x y That would be a 90º Angle x y That would be a 180º Angle

Angles of Rotation x y That would be a 270º Angle x y That would be a 360º Angle

Angles of Rotation x y An Angle of 120º in standard position y x An Angle of -120º in standard position

Example: Draw an angle with the given measure in standard position. Then determine in which quadrant the terminal side lies. A. 210º b. –45º c. 510º Use the fact that 510º = 360º + 150º. So the terminal side makes 1 complete revolution and continues another 150º. Terminal side is in Quadrant III Terminal side is in Quadrant IV Terminal side is in Quadrant II 210º –45º 510º 150º

510º 150º 510º and 150º are called coterminal (their terminal sides coincide). An angle coterminal with a given angle can be found by adding or subtracting multiples of 360º. So if you are asked to find coterminal angles you can simply add 360 to the angle or subtract 360 from the angle

Find two angles that are coterminal with 130º (one positive and one negative 130º + 360º = 490º 130º - 360º = -290º

Complimentary and Supplementary Angles 2 angles that are complimentary add up to equal 90 degrees 2 angles that are supplementary add up to equal 180 degrees Find the supplement to an angle of 24º 180 – 24 = 156 Find the compliment to an angle of 24º 90 – 24 = 66