Angles Arc Length Sector Area Section 4.1. Objectives I can find co-terminal angles I can convert between radian and degree measures I can calculate arc.

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Presentation transcript:

Angles Arc Length Sector Area Section 4.1

Objectives I can find co-terminal angles I can convert between radian and degree measures I can calculate arc length and sector area

Co-terminal Angles An angle of xº is co-terminal with angles of xº + k · 360º where k is an integer. An angle of x R is co-terminal with angles of x R + k · 2π R where k is an integer.

Section 4.1: Figure 4.4 Co-terminal Angles

Find 1 positive and 1 negative co-terminal angle

Conversion between Degrees and Radians Using the basic relationship  radians = 180º, To convert degrees to radians, multiply degrees by (  radians) / 180  To convert radians to degrees, multiply radians by 180  / (  radians)

Example 1 Convert each angle in degrees to radians 40º 75º -160º

Example cont. Solution: 40º = 40*  /180 = 2  /9 75º = 75*  /180 = 5  / º = -160*  /180 = -8  /9

Convert to degrees 180 degrees 45 degrees 216 degrees 105 degrees

Section 4.1: Figure 4.5, Illustration of Arc Length

Example 1 A circle has a radius of 7 inches. Find the length of the arc intercepted by a central angle of 75°

Example 2 A circle has a radius of 12 meters. Find the length of the arc intercepted by a central angle of π/6 radians

Example 1 A circle has a radius of 7 inches. Find the sector area for a central angle of 75°

Example 2 A circle has a radius of 12 meters. Find the sector area for a central angle of π/6 radians

Homework WS 8-3 Quiz Monday