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Name ____________________________________Date ______________Block _____
Adv. Math: Chapter 5
Lesson 2: Trigonometric Ratios in
Right Triangles
Objectives:
 Find the values of trigonometric ratios for acute angles of right triangles
Acute:
Complementary:
B
C
A
Trigonometric Ratios:
Trig.
Ratios
Words
Symbol
Definition
sine Θ
sin Θ
sin Θ = _________________
cosine Θ
cos Θ cos Θ = _________________
tangent Θ tan Θ tan Θ = _________________
**Mnemonic Device . . . .
Ex. 1: a) Find the values of the sine, cosine, and tangent for < B.
C
B
18m
33m
A
b) Find the values of the sine, cosine, and tangent for < A.
C
8cm
B
Reciprocal
Trig.
Ratios
15cm
Words
Symbol
Definition
cosecant
Θ
csc Θ
csc Θ = _____or ________________
secant Θ
sec Θ
sec Θ = ______or _______________
cotangent
Θ
cot Θ
cot Θ = _____or ________________
**Reciprocal Identities**
A
Ex. 3:
a) If cos Θ = ¾ , find sec Θ.
c)
b) If sin Θ = 0.8, find csc Θ.
If csc Θ = 1.345, find sin Θ.
Ex. 4:
a)
Find the values of the six trig. ratios for < P.
P
10 cm
M
7 cm
N
D
b) Find the values of the six trig. ratios for < E.
3 cm
E
7 cm
F
Special Triangles: 30-60-90 and
Θ
sin Θ
cos Θ
45-45-90
tan Θ
csc Θ
sec Θ
cot Θ
30
45
60
Cofunctions - sin Θ = cos (90-Θ)
tan Θ = cot (90-Θ)
sec Θ = csc (90-Θ)
HOMEWORK:
cos Θ = sin (90-Θ)
cot Θ = tan (90-Θ)
csc Θ = sec (90-Θ)