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4.2

Learn about right triangle trigonometry, famous triangles, evaluating trigonometric functions, calculator errors, and applications. Explore standard position, common calculator mistakes, and solve word problems.

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4.2

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  1. 4.2 Demana, Waits, Foley, Kennedy Trigonometric Functions of Acute Angles

  2. What you’ll learn about • Right Triangle Trigonometry • Two Famous Triangles • Evaluating Trigonometric Functions with a Calculator • Common Calculator Errors when Evaluating Trig Functions • Applications of Right Triangle Trigonometry … and why The many applications of right triangle trigonometry gave the subject its name.

  3. Standard Position An acute angle θ in standard position, with one ray along the positive x-axis and the other extending into the first quadrant.

  4. Trigonometric Functions

  5. Example: Evaluating Trigonometric Functions of 45º Find the values of all six trigonometric functions for an angle of 45º.

  6. Solution Find the values of all six trigonometric functions for an angle of 45º.

  7. Example: Evaluating Trigonometric Functions of 60º Find the values of all six trigonometric functions for an angle of 60º.

  8. Solution Find the values of all six trigonometric functions for an angle of 60º.

  9. Common Calculator Errors When Evaluating Trig Functions • Using the calculator in the wrong angle mode (degree/radians) • Using the inverse trig keys to evaluate cot, sec, and csc • Using function shorthand that the calculator does not recognize • Not closing parentheses

  10. Example: Solving a Right Triangle

  11. Solution

  12. Terminology • Line of sight: The line from the eye of the observer to the object • Angle of elevation: Angle between the line of sight and the horizontal when the object is above the horizontal • Angle of depression: Angle between the line of sight and the horizontal when the object is below the horizontal

  13. Word Problem 1 • A giant redwood tree casts a shadow that is 452 feet long. Find the height of the tree if the angle of elevation of the sun is 12.30

  14. Word problem solution

  15. Example 2: A 40 foot ladder leans against a building. If the base of the ladder is 15 feet from the base of the building, what is the angle formed by the ladder and the building? In relation to theta, which sides are we given? How would you set up the equation?

  16. Example 2: A 40 foot ladder leans against a building. If the base of the ladder is 15 feet from the base of the building, what is the angle formed by the ladder and the building? 40’ 15’

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