Chapter 8-4 part 1 Trigonometry

1
Chapter 8-4 part 1 Trigonometry

• This lesson has been modified from the original
  in the following ways
• 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.

2
Lesson 4 MI/Vocab

• trigonometry

• Find trigonometric ratios using right triangles.

• trigonometric ratio
• sine
• cosine
• tangent

• 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)
3
Trig Ratios

• Compares the lengths of two sides of a right
  triangle
• Sine (sin)
• Cosine (cos)
• Tangent (tan)

4
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

5
Trig Ratios
Opposite Opp
Hypotenuse Hyp
Adjacent Adj
Hypotenuse Hyp
Opposite Opp
Adjacent Adj
SOH-CAH-TOA
6
Given Rt. Triangle ABC
SOH-CAH-TOA

• Given ?A
• Sin A
• Cos A
• Tan A

• Given ?B
• Sin B
• Cos B
• Tan B

7
Given Rt. Triangle ABC
SOH-CAH-TOA

• Given ?A
• Sin A
• Cos A
• Tan A

• Given ?B
• Sin B
• Cos B
• Tan B

8
Lesson 4 CYP1
A. Find sin A.

1. A
2. B
3. C
4. D

9
Lesson 4 CYP1
B. Find cos A.

1. A
2. B
3. C
4. D

10
Lesson 4 CYP1
C. Find tan A.

1. A
2. B
3. C
4. D

11
Lesson 4 CYP1
D. Find sin B.

1. A
2. B
3. C
4. D

12
Lesson 4 CYP1
E. Find cos B.

1. A
2. B
3. C
4. D

13
Lesson 4 CYP1
F. Find tan B.

1. A
2. B
3. C
4. D

14
Using a Trig. Table
Angle Measure Sin Cos Tan Angle Measure Sin Cos Tan

15
Lesson 4 CYP2
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

1. A
2. B
3. C
4. D

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Lesson 4 CYP2
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

1. A
2. B
3. C
4. D

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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 functions equation
• Solve for the variable (cross-multiply if
  necessary)
• Calculate

18
Given Rt. Triangle ABCSolve for x
SOH-CAH-TOA
Hyp
Opp
32o
19
Given Rt. Triangle ABCSolve for y
SOH-CAH-TOA
Hyp
32o
Adj
20
Given Rt. Triangle ABCSolve for x
SOH-CAH-TOA
A
27o
y
Adj
3
B
Opp
x
C
21
Given Rt. Triangle ABCSolve for y
SOH-CAH-TOA
A
Hyp
27o
y
Adj
3
B
x
C
22
Given Rt. Triangle ABCSolve for x
SOH-CAH-TOA
C
Adj
Opp
x
12
58o
B
A
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Homework

• Chapter 8-4
• Pg 460
• 1,2,14-17,29-37,44,46,47,48
• Bring Calculators from now on!!!

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The Amazing Legend of
Chief SohCahToa
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• 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.