Solution:b. 405
o
and c. -315
o
are co-terminalwith 45
o
.
Noticethat terminalside of the first angle,-45o, is in the 4thquadrant.The last angle, 135 ois in the 2nd
quadrant.Thereforeneitherangleis co-terminalwith 45o.
Now consider 405 o. This is a full rotation,plus an additional45 degrees.So this angleis co-terminalwith
45 o. The angle-315ocan be generatedby rotatingclockwise.To determinewherethe terminalside is, it can
be helpfulto use quadrantalanglesas markers.For example,if you rotateclockwise90 degrees3 times
(for a total of 270 degrees),the terminalside of the angleis on the positivey-axis.For a total clockwisero-
tationof 315 degrees,we have315-270= 45 degreesmoreto rotate.This puts the terminalside of the angle
at the samepositionas 45o.
LessonSummary
In this lessonwe havecategorizedanglesaccordingto their size, and we haveextendedour knowledgeof
anglesto includeanglesof rotation.We havedefinedwhatit meansfor an angleto be in standardposition,
and we havelookedat anglesin standardposition,includingthe quadrantalangles.We havealso defined
the conceptof co-terminalangles.All of the ideasin this lessonwill be usedin the followinglesson,to define
the trigonometricfunctionsthat are the focusof this chapter.
Pointsto Consider
- How can one anglelook exactlythe sameas anotherangle?
- Wheremightyou see anglesof rotationin real life?
ReviewQuestions
- Determineif the angleis acute,right,obtuse,or straight.