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5.4 Defining trigonometric ratios

Math 10. 5.4 Defining trigonometric ratios. Ms. Albarico. Demonstrate an understanding of and apply properties to operations involving square roots. Relate the trigonometric functions to the ratios in similar right triangles.

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5.4 Defining trigonometric ratios

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  1. Math 10 5.4 Defining trigonometric ratios Ms. Albarico

  2. Demonstrate an understanding of and apply properties to operations involving square roots. • Relate the trigonometric functions to the ratios in similar right triangles. • Use calculators to find trigonometric values of angles and angles to find when trigonometric values are known. • * Solve problems using the trigonometric ratios. Students are expected to:

  3. A RATIO is a comparison of two numbers. For example; boys to girls cats : dogs right : wrong. In Trigonometry, the comparison is between sides of a triangle. Trigonometric Ratios

  4. We need to do some housekeeping before we can proceed…

  5. In trigonometry, the ratio we are talking about is the comparison of the sides of a RIGHT TRIANGLE. Two things MUST BE understood: 1. This is the hypotenuse.. This will ALWAYS be the hypotenuse 2. This is 90°… this makes the right triangle a right triangle…. Without it, we can not do this trig… we WILL NOT use it in our calculations because we COULD NOT do calculations without it.

  6. Now that we agree about the hypotenuse and right angle, there are only 4 things left; the 2 other angles and the 2 other sides. If we look at angle A, there is one side that is adjacent to it and the other side is opposite from it, and of course we have the hypotenuse. A We will refer to the sides in terms of their proximity to the angle hypotenuse adjacent opposite

  7. If we look at angle B, there is one side that is adjacent to it and the other side is opposite from it, and of course we have the hypotenuse. hypotenuse opposite B adjacent

  8. Remember we won’t use the right angle X

  9. θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’. Don’t let it scare you… it’s like ‘x’ except for angle measure… it’s a way for us to keep our variables understandable and organized. One more thing…

  10. Here we go!!!!

  11. Key Terms:

  12. Trigonometric Ratios

  13. Values of Trigonometric Function

  14. One more time… Here are the ratios: S O sinθ = opposite side hypotenuse H A C cosθ = adjacent side hypotenuse H O T tanθ = opposite side adjacent side A SOH CAH TOA

  15. Let’s Practice…. Write the ratio for sin A Sin A = a c Write the ratio for cos A Cos A = b c Write the ratio for tan A Tan A = a b B c a C b A Let’s switch angles: Find the sin, cos and tan for Angle B: Sin B = b c Tan B = b a Cos B = a c

  16. Calculator Commands Set your calculator to ‘Degree’….. MODE (next to 2nd button) Degree (third line down… highlight it) 2nd Quit

  17. 8 A 4 Practice some more… Find tan A: 24.19 12 A 21 Tan A = opp/adj = 12/21 Tan A = .5714 Find tan A: 8 Tan A = 8/4 = 2

  18. Solving Angles

  19. Note: Calculator Commands Reminder Set your calculator to ‘Degree’….. MODE (next to 2nd button) Degree (third line down… highlight it) 2nd Quit

  20. Opp’ C xo Adj’ A B To solve for Angles: Now we need to look at the two ratios involving the hypotenuse: hyp’ Opposite sin xo = Hypotenuse Adjacent cos xo = Hypotenuse

  21. Calculator Commands • For Trigonometric Inverse Functions: • 1) Press 2ND, use SIN for SIN-1 COS for COS-1 TAN for TAN-1

  22. 14.8cm b o 9.7cm Calculate the angle b o below. h (1) Identify the two sides marked. a (2) Choose the correct trig ratio . (3) Substitute in values . (4) Calculate the ratio(3 decimal places). (5) Use the inverse cosine function on your calculator to calculate the angle . b o = 49.1o

  23. Remembering the Trigonometric Ratios: Look again at the three trig ratios given below: Take the first letter of each word. Write the letters in order. S O H C A H T O A

  24. Let’s Practice…. Find an angle that has a tangent (ratio) of 2 3 Round your answer to the nearest degree. C 2cm B 3cm A Process: I want to find an ANGLE. I was given the sides (ratio). Tangent is opp adj Solution: TAN-1(2/3) = 34°

  25. Ok… we’ve found side lengths, now let’s find angle measures. Refer to your table… what function will we use to find angle measures? SIN-1 COS-1 TAN-1 These are called INVERSE FUNCTIONS.

  26. Homework! In your notebook, CYU # 18, 19, 20, 21, 22, 24, and 25 on pages 239-240.

  27. Class Work In your notebook, solve the following: CYU # 12, 13, 14, 15, 16 on pages 236-237.

  28. Work Period • Work with your group members about the final design of your pet house. • Remember : Your scale drawing must be accurate and precise.

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