Right Triangles and Trig Ratios

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Right Triangles and Trig Ratios
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SOH-CAH-TOA

• SOH-CAH-TOA is an acronym used in Geometry and
  Right Triangle Trig to remember what sides of a
  right triangle go with which Trig Ratios
• Each angle value (radians and degrees) has a
  specific ratio of sides that always holds true

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Consider an angle whose terminal ray passes
through the point (4, 5)

• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
  positive or negative for this angle (in Q1)

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Consider an angle whose terminal ray passes
through the point (-4, 5)

• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
  positive or negative for this angle (in Q2)

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Consider an angle whose terminal ray passes
through the point (-4, -5)

• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
  positive or negative for this angle (in Q3)

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Consider an angle whose terminal ray passes
through the point (4, -5)

• In which quadrant does this angle fall?
• Tell whether the sine, cosine and tangent are
  positive or negative for this angle (in Q4)

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Trig Definitions/Ratios

• Since the opposite always refers to the vertical
  distance and the adjacent always refers to the
  horizontal distance, we can say that

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Sign Analysis Chart
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Examples

• Tell whether each of the following is positive or
  negative

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Examples

• Tell whether each of the following is positive or
  negative

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Examples

• Tell whether each of the following is positive or
  negative

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Examples

• Tell whether each of the following is positive or
  negative

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Finding Exact Values

• If is a 4th quadrant angle and
  , find and

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Finding Exact Values

• An angle has a terminal ray that passes through
  the point (-4, 7). Find the exact value of the
  three trig ratios in simplest form.

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The Unit Circle(Quadrantal Angles)

• Consider a circle with radius ____
• What is the sin 90?
• Does the size of the circle matter when
  evaluating the trig ratios?

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The Unit Circle(Quadrantal Angles)
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Examples

• Find the exact value for each of the following

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Examples

• Find the exact value for each of the following

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Examples

• Find the exact value for each of the following

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Examples

• Find the exact value for each of the following

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Homework

• Pg. 272 (1 27odd)