Arc Length and Radians Agenda 1 Do Now

Arc Length and Radians Agenda 1. Do Now 2. Quiz Review 3. What is a radian? 4. Converting to radians 5. Debrief DO NOW 3/23: Mr. Mc. Laren wants a 60 degree slice of a pizza with a radius of 15 inches. How many inches will the crust of his slice be?

Quiz Review ✤ DIAGRAMS AND EQUATIONS FIRST!

What is a radian? ✤

Investigation: Radians Arc Length Radius Arc Length/Radius

How to convert radians to degrees ✤ **MUST BE IN NOTES!**

Independent Practice/Debrief ✤ How are degrees and radians related? ✤ What is the measure of 45 degrees in radians?

Learning Target: I can create a unit circle and use it to convert degrees to radians. Radians and Unit Circle Agenda 1. Do Now 2. HW Review 3. Create a unit circle 4. Label degrees/radians 5. Debrief Do Now 3/24: What is the measure of 1 radian in degrees?

HW Review: Radians Degrees

Create a Unit Circle 1. Use the record to trace a circle on the coordinate grid paper. 2. Starting with 0 on the positive x axis, use a protractor to mark off every 15 degrees (all the way to 360!) 3. Convert each angle measure from degrees to radians and label these as well.

Debrief ✤ What patterns do you notice in your unit circle? ✤ How can these patterns be related to trigonometry?

Do Now 3/25: Find the length of the segment. Learning Target: I can compare/contrast Pythagorean theorem and distance formula to derive the equation of a circle on the coordinate grid. Equation of a Circle Agenda 1. Do Now 2. Calculating the Radius of your Circle 4. Equation of Circle 5. Debrief

Unit Circle 1. Choose a coordinate that lies on your circle. 2. Connect that point with the center point to create a radius. • 3. Draw a right triangle using the radius as the hypotenuse. 4. Find the lengths of the legs of your right triangle. 5. Use the lengths of your legs to find the lengths of your radius. a 2 + b 2 = c 2

Equation of a Circle ✤ What if we have limited information? For example, only are given the coordinates of the center and the point on the edge? 1. Center (0, 0) and point (4, 8) (6, 6) 2. Center (3, 4) and point (8, 11) (2, 3) (x 1 - x 2)2 + (y 1 - y 2)2 = d 2

Equation of a Circle ✤ a 2 + b 2 = c 2 ✤ (x 1 - x 2)2 + (y 1 - y 2)2 = d 2 ✤ How can we use these two equations to help us derive a formula for the radius of a circle with center point (h, k) and a point (x, y) on the circle? Equation of a Circle (x-h)2 + (y-k)2 = r 2 **MUST BE IN NOTES!**

Equation of a Circle: Debrief/Exit Ticket 1. Write the equation of a circle with center point (2, 0) and a radius of 10. 2. Write the equation of a circle with center point (3, 6) and contains the point (0, -2)

Learning Target: I can use the coordinate grid to relate circles and right triangle trigonometry Circle Equation and Trigonometry Agenda 1. Do Now 2. Circle Equation Practice 3. Unit Circle and Trig 4. Debrief DO NOW 3/26: Identify the center and radius for the circle equation below. Then sketch the graph.

Circle Equation Practice

QUICK Trig Review ✤

Circles and Trigonometry ✤ ✤ On your circle, choose a coordinate and draw a right triangle. Label the opposite, adjacent, and hypotenuse of that right triangle, using the central angle as theta. ✤ What is another way we can describe the opposite side of this triangle on the coordinate grid? The adjacent? What is the hypotenuse in the circle? ✤ How can we represent the trigonometric ratios (sine, cosine, tangent) using a circle? • y x

Exit Ticket 1. Choose a coordinate on your circle; 2. draw a right triangle to that coordinate; 3. use trigonometry to find the measure of the angle; 4. then convert the angle to radians. ✤ BONUS: Write the equation of your circle and use your coordinate to prove the length of the radius.

Debrief Learning Target: I can use the coordinate grid to relate circles and right triangle trigonometry ✤ How can we use trigonometry to discuss angles in circles? ✤ What do the ratios of sine, cosine, and tangent represent in terms of a circle?