1.3 Definition 1 of Trigonometric Functions JMerrill, 2009.
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Transcript of 1.3 Definition 1 of Trigonometric Functions JMerrill, 2009.
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1.3 Definition 1 of Trigonometric
Functions
JMerrill, 2009
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Trigonometry The word trigonometry comes from
two Greek words, trigon and metron, meaning “triangle measurement”. We will “measure” triangles by concentrating on their angles.
Definition 1 ONLY works for right triangles
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Trigonometric Functions (Ratios) There are six trigonometric functions:
Sine abbreviated sin--sinθ Cosine abbreviated cos--cosθ Tangent abbreviated tan--tanθ Cosecant abbreviated csc--cscθ Secant abbreviated sec--secθ Cotangent abbreviated cot--cotθ
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Recall from 1.2 We discussed the ratios of the sides
of similar triangles The three main trigonometric
functions should be learned in terms of the ratios of the sides of a triangle.
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Right Triangle Trig
SOH-CAH-TOA Sin θ = Cos θ = Tan θ =
These are the ratios of 2 sides with respect to an angle.
In order to find the other trig functions, we must look at some identities
ppositeypoteO
H nuse
djacentypoteA
H nuse
OA
ppositedjacent
θ
oppositehypotenuse
adjacent
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Fundamental Trigonometric IdentitiesReciprocal Identities
1csc
sin
1
seccos
1cot
tan
Also true:
1sin
csc
1
cossec
1tan
cot
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Example Find the following—exact answers
only D
4 5 Sin D = Sin G =
Cos D = Cos G =
O 3 G Tan D = Tan G =
35
4534
453543
Board Example
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Cofunctions Notice the co in cosine, cosecant, and
cotangent. These are cofunctions and they are based on the relationship of complementary angles.
The Cofunction Theorem states that if α+β = 90o, then: sin β = cos α
sec β = csc αtan β = cot α
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Cofunction Examples Sin 30o =
Csc 40o =
Tan x =
Cos 60o
Sec 50o
Cot (90o-x)
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Fundamental Trigonometric Identities
Cofunction Identities
sin cos 90o cos sin 90o
tan cot 90o cot tan 90o
sec csc 90o csc sec 90o