Trigonometry

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Trigonometry

• Review of Pythagorean Theorem
• Sine, Cosine, Tangent Functions
• Laws of Cosines Sines

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Pythagorean Theorem
Relationship among the lengths of sides.

• c2 a2 b2
• a2 c2 - b2
• b2 c2 - a2

Side a
Side c
Side b
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Right triangles in Trigonometry

• The letters a, b, and c are lengths of sides.
• The Letter A is the measure of an angle.

A Right Triangle
c
a
b
A
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Trig functions and the right /\

• Sine (A) opposite side / Hypotenuse
• Cosine (A) adjacent side / Hypotenuse
• Tangent (A) opposite side / adjacent side

Trig function values are the ratios of the
lengths of sides.
c
Sin A Side a / Side c Cos A Side b / Side
c Tan A Side a / Side b
a
A
b
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Trig. Questions

• What is the sine of 30 degrees?
• Written Sin 30, its _____.
• What is the Cosine of 30 degrees?
• Written Cos 30, its _____.
• What is the tangent of 30 degrees?
• Written Tan 30, its _____.
• Note An angle may be also expressed in radians
  Set your calculator correctly.

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More Trig Questions

• What is the Inverse Sin (0.5000)?
• Use 2nd function key for Inverse.
• What is the Inverse Cos (0.8660)?
• Use 2nd function key for Inverse.
• What is the Inverse Tan (0.5774)?
• Use 2nd function key for Inverse.

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How to remember the functions

• Word Play

Sine Function SOH Cosine Function CAH Tangent
Function TOA Thus SOH CAH TOA
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An example Trig problem

• Imagine a right triangle having an angle of 30
  degrees. The other non-right angle would be 60
  degrees. The 30 degree and the 60 degree angles
  would be called complementary angles. Let the
  hypotenuse equal 10 m. Calculate the length of
  the opposite and adjacent sides.
• Well how are you going to do it?

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Calculating the hypotenuse.
Sin 30 degrees opp / hyp Opp hyp Sin 30
degrees opp 10 m Sin 30 deg
Opp 5.0 m Adj 8.66 m
Cos 30 degrees adj / hyp Adj hyp cos 30
degrees Adj 10 m Cos 30 deg
Hyp
10 m
30 degrees
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Trigonometry Tables

• Many people have figured out the right angle trig
  function values and published them in table form.
  Often these tables can be seen in the backs of
  trigonometry textbooks, physics textbooks, and
  engineering textbooks. Calculators now have these
  function built on to them too.
• Go To www.google.com and look for trigonometry
  tables or check a textbook.

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Law of Cosines

• Says c2 a2 b2 - 2 a b Cos C
• A, B, and C are interior angles
• and a, b, c are the lengths of the sides that are
  opposite each angle respectively.

C
a
b
B
A
c
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Law of Sines

• Says a / Sin A b / sin B c / sin C
• Where A, B, and C are interior angles
• and a, b, c are lengths of sides.

A
b
c
B
C
a