4_2Coterminalandrelatedangles.notebook

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4.2CoTerminal

andRelatedAngles

LearningGoal:

Torecognizehowanglesarerelatedbetweenallfourquadrants.

4_2Coterminalandrelatedangles.notebook

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Findtheangleofrotationandstateall3ratiosifterminalarmgoesthrough(7,12)

7

12

r2=x2+y2r=(-7)2 + 122 = 49 + 144 = 193

Sin=12 Cos=7 Tan=12193 193 7

AngleofRotation: Sin=12 =sin1(12/193)193 =59.7o

Soangleofrotationis18059.7=120.3o

angleofrotation

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r

x

y

r2=x2+y2therefore,

r=x2+y2

rrepresentsradius,whichcanonlybe+ivethereforerootalwaystakesthe+iveform.

Sin=y=opp rhyp

Cos=x=adj rhyp

Tan=y=opp xadj

InSummary:

AlwaysRemembertheCASTRulewhenworkingwithrelatedangles!

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Example1:Giventhattheterminalarmgoesthroughthepoint(4,3),findtheangleofrotationandstateallthreeprimaryratios.

(4,3)

4

3

Angleofrotation

r=(-4)2 + (3)2 = 16 + 9 = 25 = 5

Therefore,Sin = 3 Cos = -4 Tan = 3 5 5 -4

Using+iveratio Sin=3/5=sin1(3/5)=36.9referenceangle

Therefore,angleofrotation=18036.9=143.1o

NOTE:Referenceangleisfoundinsidethetriangleandisfoundusingthepositiveratio.

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Ex 2. Determine the sine of 495

(i) first we determine what quadrant the angle lies in 495-360 = 135 which is thus a second

quadrant angle

(ii) then subtract 180 - 135 = 45, so we have a 45 angle in the second quadrant

(iii) now, simply recall sin(45) = 1/2 or 2 /2

(iv) now account for the quadrant, as the sine ratio is positive in the second quadrant so the final answer is 2/2

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NOW Evaluate cos(-150)

(i) first we determine what quadrant the angle lies in

360+(-150) = 210 which is thus a third quadrant angle

(ii) then subtract 210 - 180 = 30, so we have a 30 angle in the third quadrant

(iii) now, simply recall cos(30) = 3/2 (iv) now account for the quadrant, as the cosine ratio is negative in the third quadrant so the final answer is - 3/2

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SuccessCriteria:

beabletofindmeasureofanglegivencoordinatesandquadrantusingprimarytrigratios

beabletodetermineexactmeasureofananglebasedonitsrelatedanglein1stquadrant

beabletouseaunitcircleandspecialtrianglestoaidindeterminingexacttrigratios

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Homework(refertoexamplesandkeyconceptsin

textpg232237)

Complete:CommunicateYourUnderstanding pg237 C1,C2,C3,C4Practisepg237239

112

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Attachments

extensionpostivenegativeangles_coterminals.ppt

Negative and Positive

Rotation

Ex 1. Determine the sine of 495

(i) first we determine what quadrant the angle lies in 495-360 = 135 which is thus a second quadrant angle

(ii) then subtract 180 - 135 = 45, so we have a 45 angle in the second quadrant

(iii) now, simply recall sin(45) = 1/2 or 2 /2

(iv) now account for the quadrant, as the sine ratio is positive in the second quadrant so the final answer is +2/2

Evaluate cos(-150)

(i) first we determine what quadrant the angle lies in 360+(-150) = 210 which is thus a third quadrant angle

(ii) then subtract 210 - 180 = 30, so we have a 30 angle in the second quadrant

(iii) now, simply recall cos(30) = 3/2

(iv) now account for the quadrant, as the cosine ratio is negative in the third quadrant so the final answer is - 3/2

Complete text book:

pg 350 #11 and

Pg 353 354 #1-2 every other, 3, 4

SMART Notebook

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