Basic Trigonometry Lecture 1

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Basic TrigonometryLecture 1
Slides created by Mr. SmithLehi High
School. Voiceover by Mr. P. McDevitt NBCC-SJ
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Objectives

• Introduce the basic Trigonometric Functions
• Introduce Pythagorean Theorem
• Examine strategies for solving Trig Problems
• Practice solving some trig problems.

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Parts of a Right Triangle
Side c
Side a
Side b
Pythagorean Theorem is c2 a2 b2
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Parts of a Right Triangle

• Imagine that you are at Angle A looking into the
  triangle

• The adjacent side is the side next to Angle A.

• The hypotenuse will always be the longest side,
  and opposite from the right angle.

• The opposite side is the side that is on the
  opposite side of the triangle from Angle A.

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Parts of a Right Triangle

• Now imagine that you move from Angle A to Angle B.

From Angle B the opposite side is the side that
is on the opposite side of the triangle.
From Angle B the adjacent side is the side next
to Angle B.
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Review
B
Hypotenuse
Opposite Side
A
? For Angle A
Adjacent Side
B
For Angle B ?
Hypotenuse
Adjacent Side
A
Opposite Side
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Trig Ratios

• We can use the lengths of the sides of a
  right triangle to form ratios. There are 6
  different ratios that we can make

The six possible ratios are
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Trig Ratios
Hypotenuse

• Each of the 6 ratios has a name
• The names also refer to an angle

Opposite
A
Adjacent
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Trig Ratios
B
Hypotenuse
If the angle changes from A to B
Adjacent
A
The way the ratios are made is the same
Opposite
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Trig Ratios
B

• Each of these ratios has an abbreviation

Hypotenuse
Opposite

• From now on we will focus on just the Sine,
  Cosine and Tangent ratios

A
Adjacent
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SOHCAHTOA
B
Hypotenuse
Here is a way to remember how to make the 3 basic
Trig Ratios
Opposite
A
Adjacent
1) Identify the Opposite and Adjacent sides for
the appropriate angle

• SOHCAHTOA is pronounced So Cah Toe Ah and it
  means
• Sin is Opposite over Hypotenuse, Cos is Adjacent
  over Hypotenuse, and Tan is Opposite over Adjacent

Put the underlined letters to make SOH-CAH-TOA
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Examples of Trig Ratios
1. First find the Sine, Cosine and Tangent
ratios for Angle P.
P
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2. Next find the Sine, Cosine, and Tangent
ratios for Angle Q
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Q
Remember SohCahToa
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Similar Triangles and Trig Ratios
P
B
20
5
12
3
A
C
Q
4
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R
These are similar triangles, since ratios of
corresponding sides are the same
Look at the 3 basic Trig ratios ? for these
2 triangles. They are equivalent.
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Similar Triangles and Trig Ratios

• Triangles are similar if the ratios of the
  lengths of the corresponding side are the same.
• Triangles are similar if they have the same
  angles
• All similar triangles have the same trig ratios
  for corresponding angles

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Recap Lecture 1

• The Basic Trig Functions are
• Sine - Cosecant
• Cosine - Secant
• Tangent - Cotangent
• These functions are merely ratios.
• Pythagorean Theorem is C2 A2 B2
• SOH CAH TOA is your friend.

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Thank You

• See you in Lecture 2