Transcript Geo Ch 8-4 pt 1 – Trigonometry

Chapter 8-4 part 1
Trigonometry
This lesson has been modified from the original in the following ways:
1.
Use of a trig. Table replaces a calculator. Students need access to a trig. table.
a) rationale: CST questions are based on table and calculators are not allowed.
Cheap accessible calculators can be used for trig. Students better understand the
process involved with inverse trig. functions
2. Illustrations have been enlarged.
3. SohCahToa replaces original introduction. Teachers should tell the story of the old chief
and his midnight encounter with a coffee table.
• trigonometry
• Find trigonometric ratios
using right triangles.
• Solve problems using
trigonometric ratios.
• trigonometric ratio
• sine
• cosine
• tangent
Standards 18.0 Students know the definitions of the basic
trigonometric functions defined by the angles of a right
triangle. They also know and are able to use elementary
relationships between them. For example, tan(x) =
sin(x)/cos(x), (sin(x))2 + (cos(x))2 = 1. (Key)
Standards 19.0 Students use trigonometric functions to
solve for an unknown length of a side of a right triangle,
given an angle and a length of a side. (Key)
Trig Ratios
• Compares the lengths of two sides
of a right triangle
• Sine
(sin)
• Cosine (cos)
• Tangent (tan)
Given Rt. Triangle ABC
• Given A
– Side a is the Opposite
– Side b is the Adjacent
– Side c is the Hypotenuse
• Given B
A
– Side a is the Adjacent
– Side b is the Opposite
– Side c is still the Hypotenuse
B
c
b
a
C
Trig Ratios
Opposite
Opp
Sin =
=
Hypotenuse Hyp
Adjacent
Adj
Cos =
=
Hypotenuse Hyp
Tan =
Opposite
Adjacent
Opp
=
Adj
O
S
H
A
C
H
O
T
A
SOH-CAH-TOA
SOH-CAH-TOA
Given Rt. Triangle ABC
Given A
a
Sin A =
c
b
Cos A=
c
a
Tan A=
b
B
Given B
Sin B =
Cos B =
Tan B =
b
c
a
c
b
a
c
A
b
a
C
SOH-CAH-TOA
Given Rt. Triangle ABC
Given A
4
Sin A =
5
3
Cos A=
5
4
Tan A=
3
B
Given B
Sin B =
Cos B =
Tan B =
3
5
4
5
3
4
5
A
3
4
C
A. Find sin A.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
B. Find cos A.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
C. Find tan A.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
D. Find sin B.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
E. Find cos B.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
F. Find tan B.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Using a Trig. Table
Find the Sine Cosine and Tangent of
Find the Sine Cosine and Tangent of
Find the Sine Cosine and Tangent of
Find the Sine Cosine and Tangent of
Angle
Measure
10
26
Sin Cos
Tan
Angle
Measure
Sin
Cos
10
56
26
72
Tan
.1736 .9848 .1763
56
.8290 .5592 1.483
.4877
72
.9511 .3090 3.077
.4384 .8988
A. Use your trig. table to find sin 48° to the nearest
ten thousandth.
A. 0.6691
B. 1.1106
C. 0.7431
D. 0.7314
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
B. Use your trig. table to find cos 85° to the nearest
ten thousandth.
A. 0.0872
B. 0.9962
C. 11.4301
D. 0.0698
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Finding Missing Side Lengths
• Decide which Trig function to use based on the
given angle measure the given side and the
unknown side
• Substitute the given information and the
unknown variable into the function’s equation
• Solve for the variable (cross-multiply if
necessary)
• Calculate
SOH-CAH-TOA
Opp
Sin 
Hyp
x
Sin32 
10
10( Sin32)  x
x  5.299
Given Rt. Triangle ABC
Solve for x
B
Hyp
10
Opp
x
32o
A
y
C
SOH-CAH-TOA
Adj
Cos 
Hyp
y
Cos32 
10
Given Rt. Triangle ABC
Solve for y
B
Hyp
10
10(Cos32)  y
y  8.48
x
32o
A
y Adj
C
SOH-CAH-TOA
Opp
Tan 
Adj
x
Tan 27 
3
3(Tan27)  x
x  1.5286
Given Rt. Triangle ABC
Solve for x
A
27o
y
Adj
3
B
C
x Opp
SOH-CAH-TOA
Adj
Cos 
Hyp
3
Cos 27 
y
1
y(Cos27)  3
3
y
Cos 27
y  3.3670
Given Rt. Triangle ABC
Solve for y
A
Hyp
y
27o
Adj
3
B
C
x
SOH-CAH-TOA
Opp
Tan 
Adj
12
Tan58 
x
1
x(Tan58)  12
12
x
Tan58
x  7.4986
Given Rt. Triangle ABC
Solve for x
C
Adj
x
Opp
12
58o
B
A
Homework
Chapter 8-4
• Pg 460
1,2,14-17,2937,44,46,47,48
• Bring Calculators
from now on!!!
The Amazing Legend of…
Chief
SohCahToa
Chief SohCahToa
• Once upon a time there was a wise old Native
American Chief named Chief SohCahToa.
• He was named that due to an chance encounter
with his coffee table in the middle of the night.
• He woke up hungry, got up and headed to the
kitchen to get a snack.
• He did not turn on the light and in the darkness,
stubbed his big toe on his coffee table….