TUC-1 Measurements of Angles “Things I’ve Got to Remember from the Last Two Years”
TUC-1 Measurements of Angles
Feb 22, 2016
TUC-1 Measurements of Angles. “ Things I ’ ve Got to Remember from the Last Two Years ”. In the coordinate plane, angles in standard position are created by rotating about the origin (the vertex of the angle). The initial ray is the positive x –axis. Terminal Ray. Initial Ray. - PowerPoint PPT Presentation
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TUC-1 Measurements of Angles
“Things I’ve Got to Remember from the Last Two Years”
PrecalculusMPH 9/11
The Coordinate Plane In the coordinate
plane, angles in standard position are created by rotating about the origin (the vertex of the angle). The initial ray is the positive x –axis.
Initial Ray
Terminal Ray
Positive Rotation – counterclockwise
Negative Rotation - clockwise
PrecalculusMPH 9/11
The Radian
Angles can also be measured in radians.
A central angle measures one radian when the measure of the intercepted arc equals the radius of the circle.
In the circle shown, the length of the intercepted arc equals the radius of the circle. Hence, the angle theta measures 1 radian.
r
r
r
PrecalculusMPH 9/11
Radians If one investigated one revolution of a
circle, the arc length would equal the circumference of the circle. The measure of the central angle would be 2 radians.
Since 1 revolution of a circle equals 360,2 radians = 360!!
PrecalculusMPH 9/11
RadiansThis implies that 1 radian 57.2958.
The coordinate plane now has the following labels.
0, 0
90, /2
180, 360, 2
270, 3/2
PrecalculusMPH 9/11
Converting from Degrees to Radians
To convert from degrees to radians, multiply by
Example 1 Convert 320 to radians.
Example 2 Convert -153 to radians.
PrecalculusMPH 9/11
Converting from Radians to Degrees
To convert from degrees to radians, multiply by
Example 1 Convert to degrees.
PrecalculusMPH 9/11
Converting from Radians to Degrees
Example 2 Convert to degrees.
Example 3 Convert 1.256 radians to degrees.
PrecalculusMPH 9/11
Coterminal AnglesAngles that have the same initial and
terminal ray are called coterminal angles.
Graph 30 and 390 to observe this.
Coterminal angles may be found by adding or subtracting increments of
360 or 2
PrecalculusMPH 9/11
Coterminal AnglesExample 1
Find two coterminal angles (one positive and one negative) for 425.
425 - 360 = 65 65 - 360 = -295
The general expression would be:425 + 360n where n I
PrecalculusMPH 9/11
Coterminal Angles Example 2
Find two coterminal angles (one positive and one negative) for
The general expression would be:
PrecalculusMPH 9/11
Coterminal Angles Example 3
Find two coterminal angles (one positive and one negative) for -3.187R.
-3.187 – 2π = -9.470R
-3.187 + 2π = 3.096R
The general expression would be:-3.187 + 2πn where n I
PrecalculusMPH 9/11
Complementary AnglesTwo angles whose measures sum to 90
or /2 are called complementary angles.
The complement of 37 is 53.
The complement of /8 is 3/8.
The complement of 1.274R is 0.297R.
PrecalculusMPH 9/11
Supplementary AnglesTwo angles whose measures sum to 180
or are called supplementary angles.
The supplement of 85 is 95.
The supplement of 217 does not exist. Why?
PrecalculusMPH 9/11
Supplementary AnglesThe supplement of /8 is 7/8.
The supplement of 2.891R is 0.251R.
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