Pre –Calc Sectors of circles Lesson 7.2

1. Pre –Calc Sectors of circles Lesson 7.2 A sector of a circle is the piece of pizza/pie that is cut out of a circular pizza/pie. 12 60 s Suppose we have a ‘sector’ -- like the one shown. When working with formulas involving sectors; r, s andθ are the variables involved. θ must always be in terms of radians to be used appropriately. Therefore, before you attempt to find s, or r or the area of a sector, first convert θ to radian measure if it is not already expressed so.

2. To change a degree measure to a radian measure, multiply by π. 180 So if the angle measure given is 300, we first convert by multiplying (30)(π.) = π. or .5235… 180 6 Now to find the ‘area’ of a sector, we can simply use the formula k = ½ rs Where ‘k’ = area, ‘r’ = radius, & ‘s’ = arc length Example 1 A sector of a circle has arc length 6 cm and area 75 cm2. Find its radius and the measure of its central angle. See example #1 on page 263 for the set up and solution.

3. Apparent size: 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— apparent size.

4. Example 2 Jupiter has an apparent size of 0.010 when it is 8 x 108 km from Earth. Find the approximate diameter of Jupiter. See example #2 on page 264 for the set up and solution of this problem. Example 3: A sector has perimeter 16 cm and area 15 cm2. Find its radius ‘r’ and arc length ‘s’. Be creative and come in to class tomorrow with a possible set up and solution to this problem