Transcript Lesson 5.2 Notes

Bell Work
1.
Find all coterminal angles with 125°
1.
Find a positive and a negative coterminal angle with 315°.
1.
Give the reference angle for 212°.
1.
Find the missing measures.
x
8
13
2.1
x
10.3
5.2 Trigonometric Ratios in Right
Triangles
What is a ratio?
A comparison of two numbers
B
3
4
3
A
5
C
The ratio of side AB to side BC can be written as 3
to 4, 3:4, or ¾. (We will use the fraction form)
Trigonometric ratios
Sine (sin)
Cosecant (csc)
Cosine (cos)
Secant (sec)
Tangent (tan)
Cotangent (cot)
Radical Review
√8
7
√3
√588
25
√15
Trigonometric Ratios
B
A
Sin C = Opposite
Hypotenuse
C
Cos C = Adjacent
Hypotenuse
Tan C = Opposite
Adjacent
Find the values of the sine, cosine,
and tangent for < B.
A
33
18
C
Sin B = opposite =
hypotenuse
Cos B = Adjacent =
hypotenuse
3√85
B
Tan B = Opposite =
adjacent
Find the values of sine, cosine, and
tangent for < A
B
sin A =
15
A
Cos A =
tan A =
8
17
C
Reciprocal Trig Ratios
• What is a reciprocal?
• What is the reciprocal of ⅓?
• What is the reciprocal of ⅔?
• What is the reciprocal of ⅘?
Reciprocal Trig Ratios
• csc α = 1
sin α
• sec α = 1
cos α
• cot α = 1
tan α
NOTE: α represents an
unknown angle measure
Reciprocal Trig Ratios
• If cos α = ½, then sec α = ____
• If sin α = ¾, then csc α = ______
• If cot α = 2, then tan α= _______
• If csc α =.35, then sin α = _____
Find the six trigonometric ratios for <P.
P
sin P =
csc P =
cos P =
sec P =
tan P =
cot P =
√149
10
M
7
N
Find the six trigonometric ratios for <E.
F
7
E
sin E =
csc E =
cos E =
sec E =
tan E=
cot E =
3
D
Special Right Triangles
30-60-90
Special Right Triangles
45-45-90
Find x and y.
Find x and y.
Find x and y.
Find x and y.
12
Find x and y.
Find x and y.
ACT Prep
A man is walking his dog on level
ground in a straight line with a
tree. The angle of elevation
from the man’s present position
to the top of a nearby telephone
pole is 30°. The angle of
elevation from the tree to the
top of the telephone pole is 45°.
If the telephone pole is 40 feet
tall, how far is the man with the
dog from the tree?
ACT prep cont…
A.1.7 feet
B.29.3 feet
C.42.3 feet
D.17.8 feet
More ACT Prep
Dec 2007 ACT
Use a calculator to find each
1. sin 52°
2. tan 37°
3. sec 123°
4. cot 41°37’
5. csc 21°15’19”
6. cos 83°51’37”
EXIT PASS
Find the EXACT value.
A
1. cos A
B
2. tan B
3. csc A
6m
C