FST Section 4.1. Tate lives three miles from school. He decided to ride his bicycle to school one nice day. If the front wheel turned at an average speed.

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Presentation transcript:

FST Section 4.1

Tate lives three miles from school. He decided to ride his bicycle to school one nice day. If the front wheel turned at an average speed of 80 rpms all the way from home to school, how long would it take Tate to get to school? How long would it take at 90 rpms? If the wheel had a diameter of 24 inches, how long would it take Tate to get to school at 80 rpms?

1. What is the formula used to determine the circumference of a circle? 2. What is a radius of a circle? 3. How many degrees are there in one full rotation/circle? 4. Which direction (clockwise or counterclockwise) is the ‘positive’ direction around a circle?

 Angle: the union of two rays with the same endpoint Rays ≡ Sides of the Angle Originating Side Terminating Side Endpoint ≡ Vertex of the Angle

 Measure of an Angle:  Size ▪ Degrees ▪ Revolutions ▪ Radians  Direction of Rotation ▪ Positive = Counter-Clockwise ▪ Negative = Clockwise

 Radians measure angles and their corresponding arc length  Radians allow us to quickly, easily and accurately convert circular distance (rpms, circumference, or angular rotation/velocity) into linear distance (mph, distance traveled)

When using both radians and degrees in (circular) problems, if it is UNSTATED which unit is being used, assume RADIANS!

 You can write the measure of an angle having many different possible magnitudes  Example: Draw an angle that represents one quarter of a revolution around a circle, counterclockwise. Write the measure of this angle in 4 different ways.

 When drawing an angle, it is important to: - Draw an angle to indicate direction of rotation - Clearly label all measurements (including units) - Recognize that, when using radians, the length of the arc around the circle and the measure of the central angle of the circle are the same

 A circle with a radius of one unit 1