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What is a radian?

What is a radian?. Materials needed: Scissors, wikistix (or string), Unit Circle templates Students cut a wikistix to the length of the radius of the circle. Use this length to develop and explore the concepts of radians how many radians in a circle

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What is a radian?

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  1. What is a radian? Materials needed: Scissors, wikistix (or string), Unit Circle templates Students cut a wikistix to the length of the radius of the circle. Use this length to develop and explore • the concepts of radians • how many radians in a circle • the relationship between radians and degrees

  2. The Unit Circle • Mark the center of the large circle. • Take a piece of string or ribbon and mark an angle with an arc length equal to one radius, how many degrees is it? • How many of these angles are in half of the circle?

  3. The Unit Circle • Definition: The angle you marked has a measure of one radian. How many radians are in half a circle? • Now fill in as much as you can on your unit circle.

  4. The Unit Circle • Using the cardstock draw and cut out one 45o-45o-90o triangle and one 30o-60o-90o triangle with a hypotenuse equal to the radius of your circles. • Label the hypotenuse of each triangle as 1 unit. • Label the leg lengths of the 45o-45o-90o triangles. • Label the leg lengths of the 30o-60o-90o triangles. • Use the triangles to mark the coordinates of the points on the circles.

  5. Other activities • The Number Line • Spaghetti and the unit circle • Unit Circle Project

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