chapter 8-4 part 1 trigonometry this lesson has been modified from the original in the following...
DESCRIPTION
Trig Ratios Compares the lengths of two sides of a right triangle Sine(sin) Cosine(cos) Tangent(tan)TRANSCRIPT
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• trigonometric ratio• sine• cosine• tangent
• Find trigonometric ratios using right triangles.
• Solve problems using trigonometric ratios.
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– Side a is the Adjacent– Side b is the Opposite– Side c is still the Hypotenuse
b
ac
CA
B
Trig Ratios
SOH-CAH-TOA
Opposite Opp Hypotenuse Hyp
Sin = =
Adjacent Adj Hypotenuse Hyp
Cos = =
Opposite Opp Adjacent Adj
Tan = =
HOS
HAC
AOT
Given Rt. Triangle ABCGiven A
Sin A =
Cos A=
Tan A=b
ac
CA
BGiven B
Sin B =
Cos B =
Tan B =
SOH-CAH-TOA
ca
cb
ba
cb
ca
ab
Given Rt. Triangle ABCGiven A
Sin A =
Cos A=
Tan A=
Given B
Sin B =
Cos B =
Tan B =
SOH-CAH-TOA
54
53
34
53
54
43
3
45
CA
B
AngleMeasure
Sin Cos Tan Angle Measure
Sin Cos Tan
10 1736. 569848. 1763. 8290. 5592. 4831.
26 4384. 8988. 4877. 9511. 3090. 0773.72
Using a Trig. TableFind the Sine Cosine and Tangent of 10Find the Sine Cosine and Tangent of 56Find the Sine Cosine and Tangent of 26Find the Sine Cosine and Tangent of 72
1. A2. B3. C4. D
0%0%0%0%
A B C D
A. 0.6691
B. 1.1106
C. 0.7431
D. 0.7314
A. Use your trig. table to find sin 48° to the nearest ten thousandth.
1. A2. B3. C4. D
0%0%0%0%
A B C D
A. 0.0872
B. 0.9962
C. 11.4301
D. 0.0698
B. Use your trig. table to find cos 85° to the nearest ten thousandth.
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
Given Rt. Triangle ABCSolve for x
y
x10
CA
B
32o
HypOppSin
xSin )32(10299.5x
1032 xSin
OppHyp
SOH-CAH-TOA
Given Rt. Triangle ABCSolve for y
y
x10
CA
B
32o
HypAdjCos
yCos )32(1048.8y
1032 yCos
Adj
Hyp
SOH-CAH-TOA
Given Rt. Triangle ABCSolve for x
y
x
3
C
A
B
27o
AdjOppTan
xTan )27(35286.1x
327 xTan
Adj
Opp
SOH-CAH-TOA
Given Rt. Triangle ABCSolve for y
y
x
3
C
A
B
27o
HypAdjCos
3)27( Cosy
273
Cosy
yCos 327
Adj
Hyp
SOH-CAH-TOA
3670.3y
1
Given Rt. Triangle ABCSolve for x
x 12
C
AB
58o
AdjOppTan
12)58( Tanx
5812
Tanx
xTan 1258 Adj Opp
SOH-CAH-TOA
4986.7x
1
Homework
Chapter 8-4• Pg 460
1,2,14-17,29-37,44,46,47,48
• Bring Calculators from now on!!!
Chief SohCahToa
The Amazing Legend of…
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….