Warm-up Using a white board, draw and label a unit circle with all degree and radian measures.

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.

Section 4.1: Figure 4.4 Co-terminal Angles

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

Length of a Circular Arc Let r be the radius of a circle and  the non- negative radian measure of a central angle of the circle. The length of the arc intercepted by the central angle is s = r  Angle must be in radians  O s r

Example 1 A circle has a radius of 7 inches. Find the length of the arc intercepted by a central angle of 2  /3 Solution: s = (7 inches)*(2  /3) =14  /3 inches

Homework WS 8-2