TRIG FUNCTIONS OF ACUTE ANGLES Section 12-2 Pages 555-560

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Transcript of TRIG FUNCTIONS OF ACUTE ANGLES Section 12-2 Pages 555-560

Trig Functions of acute angles

Trig Functions of acute anglesSection 12-2Pages 555-560Trig Functions of Acute AnglesDraw an acute angle in standard position.Choose any point (x, y) on the terminal side of and let r be the distance from the origin to (x, y)(x, y)xyrTrig Functions of Acute Angles(x, y)xyrTrig Functions of Acute AnglesAnother way to think of this is using the word:

SohCahToaAdjacentOppositeHypotenuseSin =Trig Functions of Acute AnglesAnother way to think of this is using the word:

SohCahToaAdjacentOppositeHypotenuseCos =Trig Functions of Acute AnglesAnother way to think of this is using the word:

SohCahToaAdjacentOppositeHypotenuseTan =Trig Functions of Acute Angles Find the Sin , Cos , and Tan given that is an angle in standard position passing through the point (4, 5).

45Sin ==Cos ==Tan =Trig Functions of Acute AnglesTrig Functions of Acute Angles Find the value of the six trig functions of whose terminal side passes through (5, 12)51213Sin =Cos =Tan =Csc =Sec =Cot =Trig Functions of Acute Angles Find the value of the six trig functions of whose terminal side passes through (2, 4)24Sin =Cos =Tan =2Csc =Sec =Cot =Trig Functions of Acute AnglesOral Exercises 1-4Page 559, 1-8Trig Functions of acute anglesSection 12-2Pages 555-560Trig Functions of Acute Angles Find the value of the six trig functions of whose terminal side passes through (-3,- 4)-4-35Sin =Cos =Tan =Csc =Sec =Cot =Trig Functions of Acute AnglesTrig Functions of Acute AnglesPythagorean Identities

Sin2 + Cos2 = 1

1 + Tan2 = Sec2

1 + Cot2 = Csc2

Trig Functions of Acute AnglesSin2 + Cos2 = 1

Csc = 3

Trig Functions of Acute AnglesCsc = 3

Trig Functions of Acute AnglesSin2 + Cos2 = 1

Trig Functions of Acute AnglesTrig Functions of Acute Angles Cofunction IdentitiesThe Sine and Cosine functions are called cofunctions.ABCabcSin A = Cos B = = Cos BWhat can we say about angles A and B? ComplementaryTrig Functions of Acute Angles Cofunction IdentitiesABCabcSin A = = Cos BTan A = = Cot BCsc A = = Sec BTrig Functions of Acute Angles Cofunction IdentitiesFrom these identities, note that:

Sin = Cos (90 )

Tan = Cot (90 )

Sec = Csc (90 )

Cos = Sin (90 )Cot = Tan (90 )Csc = Sec (90 )Trig Functions of Acute AnglesOral Exercises 5-8Page 559, 9-19Trig Functions of acute anglesSection 12-2Pages 555-560Trig Functions of Acute Angles So far in this section:Soh Cah ToaIdentitiesQuotient IdentitiesPythagorean IdentitiesCofunction IdentitiesTrig Functions of Acute Angles In trigonometry, there are two triangles that are used repeatedly in different problems.

30-60-90 right triangle

45-45-90 right triangle306012454511Trig Functions of Acute AnglesUsing these two triangles, we can find the following:Sin Cos Tan 304560Trig Functions of Acute AnglesUse the two triangles (or chart) to evaluate the reciprocal functions.Csc Sec Cot 30456022Trig Functions of Acute AnglesFind the lengths of the missing sides.Trig Functions of Acute AnglesFind the lengths of the missing sides.Trig Functions of Acute Angles Find the length of x. x456015hx'x'Trig Functions of Acute Angles Find the length of x. x456015x''Trig Functions of Acute Angles Find the length of x. 456015X = Trig Functions of Acute Angles Find the length of x. 301524xx'1Trig Functions of Acute Angles Find the length of x. 301524x24 -X = 24Trig Functions of Acute AnglesOral Exercises 9-12Page 559, 20-34Trig Functions of Acute AnglesTrig Functions of Acute Angles