TUC-1+Measurement+of+Angles

= = toc =Lesson Summary:= This section will teach you how to measure angles in both radians and degrees. The section covers various topics, most of which are review from previous years. The most common unit of measurement for angles is degrees, however they can also be written in radians. One radian equals 57.2958˚ and a central angle measures one radian when the measure of the intercepted arc equals the radius of the circle. Although this may seem complicated, one can convert from degrees to radians by multiplying the number by π/180//.// Also, to convert radians to degrees, just multiply by 180/π. On the coordinate plane, angles can have the same initial and terminal rays. These angles are called coterminal angles. To find coterminal angles, one must add or subtract 360˚ (degrees) or 2π (radians). There are also complementary angles and supplementary angles. Complementary angles are two angles that when added equal 90˚ or π/2 radians. These can be found by subtracting the given angle from 90˚ or π/2. Supplementary angles are when two angles, when added, equal 180˚ or π. These can be found by subtracting the given angle from 180˚ or π. = = = = =Helpful Links:=

http://www.clarku.edu/~djoyce/trig/angle.html

http://www.algebralab.org/lessons/lesson.aspx?file=trigonometry_trigdegradian.xml

=Practice Problems:=

1)
Convert 200˚ to radians 200 • __π__ 180 = __200π__ 180 = __10π__ 9

2)
Find the complement of 80˚ x + 80 = 90 __- 80 - 80__ 0 10

x=10˚ The complement of 80˚ is 10˚

3)
Convert __3π__ to degrees. 5 __3π__ • __180__ 5 π = __540π__ 5π = 108˚

4)
Find the supplement of 75˚ 75 + x = 180 __-75 -75__ 0 105 x = 105˚ =iMovie:= media type="file" key="miller-TUC.m4v" width="300" height="300"