Transcript What are Trigonometric Ratios?

D. Trigonometry
Math 10: Foundations and Pre-Calculus
FP10.4
Develop and apply the primary trigonometric ratios (sine,
cosine, tangent) to solve problems that involve right
triangles.
Key Terms:
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Find the definition of
each of the following
terms:
Angle of Inclination
Tangent Ratio
Sine Ratio
Cosine Ratio
Indirect
Measurement
Angle of Elevation
 Angle of Depression
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1. The Tangent Ratio
FP10.4
 Develop and apply the primary
trigonometric ratios (sine, cosine, tangent)
to solve problems that involve right
triangles.
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1. The Tangent Ratio
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Remember the Tan ratio?
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What is the tan ratio and what do we use
it for?
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The value of the tangent ratio is usually
expressed as a decimal that compares the
lengths of the sides
Example
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You can use a scientific calculator to
determine the measure of an acute angle
when you know the value tan ratio
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The tan-1 or Inv tan on your calculator
does this for you
Example
Example
Example
Practice
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Ex. 2.1 (p. 74) #1-20
#6-23
2. Calculating Length with Tangent
Ratio
FP10.4
 Develop and apply the primary
trigonometric ratios (sine, cosine, tangent)
to solve problems that involve right
triangles.
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The tangent ratio is a powerful tool we
can use to calculate the length of a leg of
a right triangle
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We are measuring indirectly when we
measure this way
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We can find the length of a leg of a
triangle by setting up the tangent formula,
as long as we have one of the acute angles
and the legs
Example
Example
Example 3
Practice
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Ex. 2.2 (p. 81) #1-14
#1-4, 6-16
3. Sine and Cosine Ratios
FP10.4
 Develop and apply the primary
trigonometric ratios (sine, cosine, tangent)
to solve problems that involve right
triangles.
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In a right triangle, the ratios that relate
each leg to the hypotenuse depend only
on the measure of the acute angle not the
size of the triangle
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These ratios are called the sine and
cosine ratios
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The sine ratio is written sin θ
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The cosine ratio is written cos θ
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The sine, cosine and tangent ratios are
called the primary trig ratio
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The values of the trig ratios are often
expressed as decimals
Example
Example
Example
Practice
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Ex. 2.4 (p. 94) #1-15
#1-3, 5-17
4. Using Sine and Cosine to find
Length
FP10.4
 Develop and apply the primary
trigonometric ratios (sine, cosine, tangent)
to solve problems that involve right
triangles.
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4. Using Sine and Cosine to find
Length
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Construct Understanding
p. 97
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We can use the sin and cos ratios to
write an equation that we can solve to
calculate the length of a leg in a right
triangle
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When the measure of one acute angle
and the hypotenuse are know
Example
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The sin and cosine ratios can be used to
calculate the measure of the hypotenuse
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When the measure of one acute angle
and the length of one of the legs are
known
Example
Example
Practice
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Ex. 2.5 (p. 101) #1-12
#1-14
5. Applying Trig
FP10.4
 Develop and apply the primary
trigonometric ratios (sine, cosine, tangent)
to solve problems that involve right
triangles.
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5. Applying Trig
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Construct Understanding
p. 105
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When we calculate the measures of all
the angles and all the side lengths in a
right triangle, we solve the triangles.
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We can use any of the three primary trig
ratios to do this.
Example
Example
Example
Practice
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Ex. 2.6 (p. 110) #1-14
#1-2, 5-16
6. Problems with More Triangles
FP10.4
 Develop and apply the primary
trigonometric ratios (sine, cosine, tangent)
to solve problems that involve right
triangles.
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6. Problems with More Triangles
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We can use Trig to solve problems that
can be modeled using right triangles
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When one more right triangle is involved,
we have to decide which triangle to start
with
Example
Example
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Sometimes the right triangles are not
even in the same plane
Example
Practice
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Ex. 2.7 (p. 118) #1-14
#5-21