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Right Triangles and Trig Ratios

Right Triangles and Trig Ratios. 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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Right Triangles and Trig Ratios

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  1. Right Triangles and Trig Ratios

  2. 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

  3. 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)

  4. 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)

  5. 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)

  6. 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)

  7. 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…

  8. Sign Analysis Chart

  9. Examples • Tell whether each of the following is positive or negative:

  10. Examples • Tell whether each of the following is positive or negative:

  11. Examples • Tell whether each of the following is positive or negative:

  12. Examples • Tell whether each of the following is positive or negative:

  13. Finding Exact Values • If is a 4th quadrant angle and , find and

  14. 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.

  15. 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?

  16. The Unit Circle(Quadrantal Angles)

  17. Examples • Find the exact value for each of the following:

  18. Examples • Find the exact value for each of the following:

  19. Examples • Find the exact value for each of the following:

  20. Examples • Find the exact value for each of the following:

  21. Homework • Pg. 272 (1 – 27odd)

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