Warmup:%20What%20is%20wrong%20with%20this?

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Warmup What is wrong with this?
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8.3 and 8.4 Trigonometric Ratios
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Finding Trig Ratios

• A trig ratio is a ratio of the lengths of two
  sides of a right triangle.
• The word trigonometry is derived from the
  ancient Greek language and means measurement of
  triangles.
• The three basic trig ratios are sine, cosine, and
  tangent.
• Abbreviated as sin, cos, and tan respectively

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Trigonometric Ratios

• Let ?ABC be a right triangle. If you are
  standing from angle A, the following sides are
  labeled opposite, adjacent and hypotenuse

adjacent
b
cos A

hypotenuse
c
opposite
a
sin A

hypotenuse
c
opposite
a
tan A

adjacent
b
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Trigonometric Ratios

• If you were standing at angle B, you would have
  to re-label the sides of opposite, adjacent and
  hypotenuse

adjacent
a
cos B

hypotenuse
c
opposite
b
sin B

hypotenuse
c
opposite
b
Tan B

adjacent
a
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The famous Indian

• SOHCAHTOA

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Ex. 1 Find sin, cos and tan of angle S
Ratio ?S



opposite
sin S
hypotenuse
adjacent
cosS
hypotenuse
opposite
tanS
adjacent
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Ex.2 Find the sin, cos and tan of angle R
Ratio ?R



opposite
sin R
hypotenuse
adjacent
cosR
hypotenuse
opposite
tanR
adjacent
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Using the Inverse

• You can use the sin, cos and tan ratio and
  calculate its inverse, sin-1, cos-1, tan-1 to
  find the measure of the angle.
• Make sure your calculator is in degree mode!!!
• make note sin, cos, and tan are ratios.
• Inverses find angles!!!

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Lets find angle S.
Ratio ?S



opposite
sin S
hypotenuse
adjacent
cosS
hypotenuse
opposite
tanS
adjacent
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Now lets find the angle measure from a previous
example
Ratio ?R



opposite
sin R
hypotenuse
adjacent
cosR
hypotenuse
opposite
tanR
adjacent
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Examples Given the triangles below, find the
missing angle measure to the nearest degree
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2
6
8
?
?
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Practice Solve for the missing variables

• 1.) 2.)
• 3.) 4.)

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12
x
26
m
16
9
30
p
15
y
z
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(No decimal answers in 4)