Introduction to Trigonometric Functions

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Introduction to Trigonometric Functions

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• Trig functions are the relationships amongst
  various sides in right triangles.
• You know by the Pythagorean theorem that the sum
  of the squares of each of the smaller sides
  equals the square of the hypotenuse,

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You know in the above triangle that

• Trig functions are how the relationships amongst
  the lengths of the sides of a right triangle vary
  as the other angles are changed.

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How does this relate to trig?

• The opposite side divided by the hypotenuse, a/c,
  is called the sine of angle A
• The adjacent side divided by the hypotenuse, b/c,
  is called the cosine of Angle A
• The opposite side divided by the adjacent side,
  a/b, is called the tangent of Angle A

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Remember SOHCAHTOA

• Sine is Opposite divided by Hypotenuse
• Cosine is Adjacent divided by Hypotenuse
• Tangent is Opposite divided by Adjacent
• SOHCAHTOA!!!!!!

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Table of Contents

• Examples
• Question 1
• Question 2
• Question 3
• Question 4

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Example 1If a 3 and c 6, what is the
measurement of angle A?
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Answer a/c is a sine relationship with A. Sine
A 3/6 .5, from your calculator, angle A 30
degrees.
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Example 2

• A flagpole casts a 100 foot shadow at noon. Lying
  on the ground at the end of the shadow you
  measure an angle of 25 degrees to the top of the
  flagpole.
• How High is the flagpole?

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How do you solve this question?

• You have an angle, 25 degrees, and the length of
  the side next to the angle, 100 feet. You are
  trying to find the length of the side opposite
  the angle.
• Opposite/adjacent is a tangent relationship
• Let x be the height of the flagpole
• From your calculator, the tangent of 25 is .47
• .47
• x (.47)(100), x 47
• The flagpole is 47 feet high.

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Question 1

• Given Angle A is 35 degrees, and b 50 feet.
• Find c. Click on the correct answer.
• A. 61 feet
• B 87 feet
• C. 71 feet

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GREAT JOB!

• You have an angle and an adjacent side, you need
  to find the hypotenuse. You knew that the cosine
  finds the relationship between the adjacent and
  the hypotenuse.
• Cosine 35 50/c, c Cosine 35 50,
• So c 50/cos 35, or approximately 61

Next question
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Nice try

• You have an angle and the adjacent side. You want
  to find the hypotenuse.
• What relationship uses the adjacent and the
  hypotenuse?

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Question 2

• If the adjacent side is 50, and the hypotenuse is
  100, what is the angle? Please click on the
  correct answer.
• A. 60 degrees
• B. 30 degrees
• C. 26 degrees

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Way to go!

• Given the adjacent side and the hypotenuse, you
  recognized that the adjacent divided by the
  hypotenuse was a cosine relationship.
• Cosine A 50/100,
• A 60 degrees

Next question
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Nice try

• Given an adjacent side and a hypotenuse, what
  relationship will give you the angle?

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Question 3

• If the opposite side is 75, and the angle is 80
  degrees, how long is the adjacent side?
• A. 431
• B. 76
• C. 13

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Nice job

• You were given the opposite side of 75 and an
  angle of 80 degrees and were asked to find the
  adjacent side. You recognized that this was a
  tangent relationship.
• Tangent 80 75/b,
• b tangent 80 75,
• b 13

Next question
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Nice Try

• You are given an angle and the opposite side, and
  have been asked to find the adjacent side. What
  relationship uses the opposite side and the
  adjacent side?

Back to question
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Question 4If B 50 degrees and b 100 what is
c?
B
A. 155
c
________
B. 130
a
___________
________
A
C
C. 84
b
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Nice try

• What is the relationship between B and b? And,
  what is the relationship between b and c?

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Great job!

• First, you recognized that b is the opposite side
  from B. Then, you recognized that the
  relationship between an opposite side and the
  hypotenuse is a sine relationship.
• Sine 50 100/c, c Sine 50 100, c 100/sine 50
  130.

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Introduction to Quadrants
90 degrees
II
I
180 degrees______________________ 0 degrees
__________________
IV
III
270 degrees
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Quadrants

• All angles are divided into 4 quadrants
• Angles between 0 and 90 degrees are in quadrant 1
• Angles between 90 and 180 degrees are in quadrant
  II
• Angles between 180 and 270 degrees are in
  quadrant III
• Angles between 270 and 360 degrees are in
  quadrant IV
• Why is this important? Click and find out!

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Importance of quadrants

• Different trig functions are positive and
  negative in different quadrants.
• The easy way to remember which are positive and
  negative in each quadrant it to remember, All
  Students Take Classes

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All Students Take Classes

• Quadrant I 0 90 degrees All All trig
  functions are positive
• Quadrant II 90 180 degrees Students Sine
  functions are positive
• Quadrant III 180 270 degrees Take Tangent
  functions are positive
• Quadrant IV 270 360 degrees Classes Cosine
  functions are positive

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Standard Angle Values
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Remember

• Simplify the fractions
• Place the radicals in the numerator. Write
• Instead of

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Congratulations

• You have learned how to use the 3 main trig
  functions, you have learned which functions are
  positive in which quadrants, and you have learned
  values of sine, cosine, and tangent for 5
  standard angles.

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