4.1(a) Notes: Constructing the Unit Circle

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Presentation transcript:

4.1(a) Notes: Constructing the Unit Circle Date: 4.1(a) Notes: Constructing the Unit Circle Lesson Objective: Construct radians and the unit circle. CCSS: F-TF Extend the domain of trigonometric functions using the unit circle. You will need: compass, colored pens

Lesson 1: Radians Use a ruler to draw a diameter horizontally across your circle. Label the points on the circle (1, 0) and (-1, 0). With the candy, measure the radius and tear off any excess candy. Starting at (1, 0), measure in radians on the circle using the candy. Mark each radian on the circle in red.

Lesson 1: Radians

Lesson 1: Radians

Lesson 1: Radians Definition of Radian: The measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. θ = 𝒔 𝒓 where θ is measured in radians. 1 revolution = circumference: s = 2πr ½ revolution = ¼ revolution = ⅙ revolution =

Lesson 2: The Unit Circle Using a compass, construct a line perpendi-cular to the diameter. Label the points (0, 1) and (0, -1). Also label the points in degrees and radians. In quadrant I, construct a 45°. Draw the line through the center to the other side of the circle. Label the degrees and radians.

Lesson 2: The Unit Circle

Lesson 2: The Unit Circle In quadrant I, construct a 60° angle. Draw the line through the center to the other side. Label the Label the degrees and radians. In quadrant I, construct a 30° angle. Draw the line through to the other side. Label the degrees and radians. Follow steps B-D in quadrant II to complete the unit circle. Label all points on the circle.

Lesson 2: The Unit Circle

Lesson 3: Converting Degrees to Radians Using π radians = 180°, 1) To convert degrees to radians, multiply degrees by π radians 180° 2) To convert radians to degrees, multiply radians by 180° π radians Hint: The unit you are converting to is on the top because you need to cancel the old units.

Lesson 3: Converting from Degrees to Radians Hint: The unit you are converting to is on the top because you need to cancel the old units. Convert each angle in degrees to radians. 60° 270° -300°

Lesson 3: Converting from Degrees to Radians Hint: The unit you are converting to is on the top because you need to cancel the old units. Convert each angle in radians to degrees. D. 3π radians 4 E. – 4π radians 3 F. 6.283 radians

Lesson 4: Negative Angles

4.1(a): Do I Get It? Yes or No Convert to radians. 135° 4. 1/10 revolution 540° 5. 1/9 revolution -270° 6. 1/15 revolution Convert to degrees. -π/2 rad 10. 1/10 revolution 9π/2 rad 11. 1/9 revolution 2 rad 12. 1/15 revolution