Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?

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Presentation transcript:

Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?

Picture 1Picture 2Picture 3 Where is vertex? Name of Angle Formula:

Identify the type of angle. Then, find the missing value. ? ?

? ?

? ? ?

How can we measure the length of a football field? Just as we can measure a football field in yards or feet, we can measure a circle in more than one way!

Introducing… Radians! You’re used to thinking of a circle in terms of degrees: 360° is the whole circle. 180° is half the circle, etc... Radian measure is just a different way of talking about a circle.

Think about what the word radian sounds like… It turns out that a radian has a relationship to the radius of a circle!

That’s why the circumference of a circle can be found using the formula: You’ve seen radians without even knowing it!

Converting Remember: Where you are going is more important than where you are coming from! Given radians: Given degrees:

Arc Length An arc of a circle is a portion of the circumference formed by a central angle. It’s the length of the pie crust! θ

Arc Length The arc length s of a circle radius r, subtended by a central angle of θ radians, is given by: s = rθ The angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!

Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian. Example 1: Arc Length “Subtended?” That just means “formed by.”

Area of a Sector A sector of a circle is a portion of the circle formed by a central angle. It’s the area of a slice of pie! θ

Area of a Sector The area of a sector A of a circle radius r, subtended by a central angle of θ radians, is given by: A = ½r 2 θ Again, the angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!

Find the area of the sector of a circle of radius 5 feet subtended by an angle of 60°. Round the answer to two decimal places. Example 2: Area of a Sector “Subtended?” That just means “formed by.”

Put it all together! Arc Length Area of a Sector s = rθ A = ½r 2 θ Length of pie crust Area of a slice