Lesson 7-2 Sectors of Circles.

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Presentation transcript:

Lesson 7-2 Sectors of Circles

Objective:

Objective: To find the arc length and area of a sector of a circle and to solve problems involving apparent size.

A sector of a circle is the piece of pizza/pie that is cut out of a circular pizza/pie.

Suppose we have a sector like the one shown: 12 s 60°

Suppose we have a sector like the one shown: When working with formulas involving sectors; r, s and θ are the variables involved. θ must always be in terms of radians to be used appropriately. 12 s 60°

Suppose we have a sector like the one shown: Therefore, before you attempt to find s, r, or the area of a sector; first convert θ to radian measure if it is not already done so. 12 s 60°

To change a degree measure to a radian measure, multiply by

To change a degree measure to a radian measure, multiply by

So, if the angle measure given is 600; we first convert by multiplying

So, if the angle measure given is 600; we first convert by multiplying

Now to find the area of a sector, we can simply use the formula:

Now to find the area of a sector, we can simply use the formula:

A sector of a circle has arc length 6 cm and area 75 cm2 A sector of a circle has arc length 6 cm and area 75 cm2. Find its radius and the measure of its central angle.

When there is nothing in our field of vision against which to judge the size of an object, we perceive the object to be smaller when it is farther away. For example, the sun is much larger than the moon, but we perceive the sun to be about the same size as the moon because the sun is so much farther from Earth.

So, how big an object looks depends not only on its size but also on the angle that it subtends at our eyes.

The measure of this angle is called the object’s So, how big an object looks depends not only on its size but also on the angle that it subtends at our eyes. The measure of this angle is called the object’s apparent size.

Jupiter has an apparent size of 0.01° when it is 8 x 108 km from Earth. Find the approximate diameter of Jupiter.

A sector has perimeter 16 cm and area 15 cm2 A sector has perimeter 16 cm and area 15 cm2. Find its radius r and arc length s.

Assignment: Pg. 265 C.E. 1-4 all W.E. 1-15 odd