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1.3 Definition 1 of Trigonometric
Functions
JMerrill, 2009
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
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
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.
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
Fundamental Trigonometric IdentitiesReciprocal Identities
1csc
sin
1
seccos
1cot
tan
Also true:
1sin
csc
1
cossec
1tan
cot
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
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
Cofunction Examples Sin 30o =
Csc 40o =
Tan x =
Cos 60o
Sec 50o
Cot (90o-x)
Fundamental Trigonometric Identities
Cofunction Identities
sin cos 90o cos sin 90o
tan cot 90o cot tan 90o
sec csc 90o csc sec 90o