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Warm-Up

Warm-Up. The infield of a baseball field is a square. The distance from home plate to first base is 90 feet. What is the distance from home plate to second base? What is the distance from third base to first base?

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Warm-Up

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  1. Warm-Up • The infield of a baseball field is a square. The distance from home plate to first base is 90 feet. • What is the distance from home plate to second base? • What is the distance from third base to first base? • What is the distance to the pitcher’s mound if it is equidistant from all the bases?

  2. Radian/Degree Conversions A love story

  3. Learning Outcomes • I will be able to discuss angle measures in terms of degrees or radians • I will be able to convert between radians and degrees • I will be able to fill in a unit circle for both degrees and radians.

  4. What are radians? • Radians are a way to measure angles as the distance around a unit circle. • What is a unit circle? • A unit circle is a circle with a radius of 1.

  5. Why do we use radians? • We use radians because at higher levels of math, radians are much easier to use for functions when compared to degrees.

  6. How do we use radians? • Suppose we have a unit circle. What is the distance around the circle? C = 2πr or in the case of a unit circle C = 2π • Well what is the distance around a circle in degrees? 360°

  7. How do we use radians? • This means that our conversion factor looks like this… or if we simplify • We can use this to create an equation for finding radians or degrees. rad = deg ∙ deg = rad ∙

  8. How do we use radians? • Let’s try to convert degrees to radians. 90° 60° 40° 270° Remember: rad = deg ∙ rad = deg ∙ rad = 90° ∙ rad = rad = deg ∙ rad = 60° ∙ rad = rad = deg ∙ rad = 40° ∙ rad = rad = deg ∙ rad = 270° ∙ rad =

  9. How do we use radians? • Let’s try to convert radians to degrees. Remember: deg = rad ∙ deg = rad ∙ deg = ∙ deg = 45º deg = rad ∙ deg = ∙ deg = 30º deg = rad ∙ deg = ∙ deg = 72º deg = rad ∙ deg = ∙ deg = 240º

  10. Think Radians Worksheet

  11. The Unit Circle • What is a unit circle? • A unit circle is a circle with a radius of 1. • If our goal is to find coordinates of the unit circle what information might we be able to use?

  12. The Unit Circle

  13. Exit Ticket Homework • Convert 45º to radians. • Convert to degrees. • Finish Think Radians Worksheet and Blank Unit Circle • QUIZ NEXT CLASS!!!

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