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Trigonometry Review: Warm-Up & Homework Questions

Get a head start on trigonometry concepts with this review including right triangles, trigonometric functions, special angles, Pythagorean triples, and more. Master the basics before the upcoming quiz and test your knowledge with practice problems. Don't forget to memorize the trig values and understand inverse trig functions for a complete understanding.

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Trigonometry Review: Warm-Up & Homework Questions

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  1. Warm-Up: January 16, 2014 • Given that and find the value of the cosθ

  2. Homework Questions?

  3. Trig Value Table • Memorize it! • Quiz 1st week of 2nd semester • 8 minute time limit • All or nothing • 20 points • There are a lot of patterns • We will go over all of the patterns before the quiz

  4. Right Triangle Trigonometry Section 4.3

  5. Right Triangles • A right triangle has a 90˚ angle and two acute angles B c = length of the hypotenuse a = length of side opposite of θ θ A C b = length of side adjacent to θ

  6. Trigonometric Functions SOH-CAH-TOA

  7. More Trigonometric Functions

  8. Example 1 • Find the value of each of the trigonometric functions of θ. B c 3 θ A C 4

  9. You-Try #1 • Find the value of each of the trigonometric functions of θ. B c 5 θ A C 12

  10. Pythagorean Triples • Pythagorean triples are integer side lengths of a right triangle • 3-4-5 • 5-12-13 • 7-24-25 • 8-15-17 • And many more • And any multiple of any of them (such as 6-8-10)

  11. Trig Values of Special Angles

  12. Assignment • Page 461 #1-19 odd • No calculator

  13. First Few Problems • In Exercises 1-8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then, find the value of each of the six trigonometric functions of θ. 5) B B B 3) 26 29 1) 9 10 θ θ θ A A A C C C 12 21

  14. Warm-Up: January 17, 2014 • Find the value of each of the trigonometric functions of θ. B 17 a θ A C 15

  15. Homework Questions?

  16. Cofunctions • The value of a trig function of an angle is equal to the value of the cofunction of the complement of the angle • If θ is in radians, replace 90˚ with

  17. Example 4 • Find a cofunction with the same value as the given function.

  18. You-Try #4 • Find a cofunction with the same value as the given function.

  19. Trig Functions on TI-83 • All scientific and graphing calculators should have buttons for sin, cos, and tan. • Most do not have csc, sec, and cot. • Make sure that your calculator is set to the correct angle measure (degrees or radians) • TI-83: Press [MODE] and make sure the correct one of “Radian” or “Degree” is highlighted

  20. Angles of Elevation & Depression • The angle formed by a horizontal line and the line of sight to an object that is above the horizontal line is the angle of elevation. • The angle formed by a horizontal line and the line of sight to an object that is below the horizontal line is the angle of depression. angle of depression

  21. Example 5 • Sighting the top of a building, a surveyor measured the angle of elevation to be 24˚. The transit is 5 feet above the ground and 250 feet from the building. Find the building’s height (to the nearest foot).

  22. You-Try #5 • At a certain time of day, the angle of elevation of the sun is 39˚. A tree casts a shadow 37 feet long. Find the tree’s height (to the nearest foot).

  23. Assignment • Page 462 #21-33 odd, 43-49 odd • Calculator required

  24. First Few Problems • In Exercises 21-28, find a cofunction with the same value as the given expression.

  25. Warm-Up: January 27, 2014 • At a certain time of day, the angle of elevation of the sun is 59˚. A tree casts a shadow 24 feet long. Find the tree’s height (to the nearest foot).

  26. Homework Questions?

  27. Unit Circle Quiz! • Clear everything off of your desk except a pencil and eraser. • 5 minute time limit • All or nothing • Must be turned in by the end of 5 minutes • Do NOT begin until instructed to do so. • Any talking while any quiz is out will result in a zero.

  28. Unit Circle Quiz! • Clear everything off of your desk except a pencil and eraser. • 5 minute time limit

  29. Inverse Trig Functions • If , then • “Theta equals the inverse sine of x” • Other inverse trig functions follow the same format • TI-83: [2nd] [sin]

  30. Example 6 • The Washington Monument is 555 feet high. If you stand ¼ mile away (1320 feet), and look at the top, what is the angle of elevation (to the nearest degree)?

  31. You-Try #6 • A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

  32. Assignment • Page 462 #35-42 ALL

  33. Assignment Problems • In Exercises 35-38, use a calculator to find the value of the acute angle θ to the nearest degree. • In Exercises 39-42, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places.

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