Math 9_ Week 5 - Introduction to Trigonometry.pptx

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1. TRIGONOMETRY An Introduction to

2. In all the situation distances or heights can be measured by using some mathematical techniques which comes under a branch of mathematics called trigonometry. Trigonometry is derived from Greek words: Tri + gon + metron (three) (sides) (measure) In fact, Trigonometry is the study of relation between the sides and angles of a triangle.

3. HISTORICAL BACKGROUND The history of trigonometry dates back to the early age of Egypt and Babylon. Angles were then measured in degree. It was then advanced by the Greek astronomer Hipparchus in the 2 nd century B.C who compiled a trigonometric table that measured the length of chord subtending a various angles in a circle of a fixed radius “r”.

4. Hipparchus is considered the greatest astronomical observer , and by sone, the greatest astronomer of antiquity . He was the first Greek to develop quantitative and accurate models for the motion of the sun and moon . With his solar and lunar theories and his numerical trigonometry. He was probably the first to develop reliable method to predict solar eclipses .

5. TRIGONOMETRIC FUNCTIONS SOH-CAH-TOA CHO-SHA-CAO

6. MEMORIZE: SOH-CAH-TOA CHO-SHA-CAO

7. The Trigonometric Functions we will be looking at SINE COSINE TANGENT

8. The Trigonometric Functions SIN E COS INE TAN GENT

9. SIN E Pronounced “sign”

10. Pronounced “co-sign” COS INE

11. Pronounced “tan-gent” TAN GENT

12. Pronounced “theta” Greek Letter θ Represents an unknown angle

13. opposite hypotenuse adjacent hypotenuse opposite adjacent

14. We need a way to remember all of these ratios…

15. Some Old Hag Came Around Here Taking Our Apples

16. Finding sin, cos, and tan

17. 6 8 10 SOH CAH TOA

18. TO CHECK WE NEED TO USE OUR CALCULATOR HERE’S HOW: On your calculators or cellphones locate the sin, cos or tan. Locate “shift” or “inv” Press “shift” or “inv” Press sin, cos or tan Type in the fraction Close the bracket Press equal sign. Round off to the nearest whole number.

19. Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 9 6 10.8 A

20. Find the values of the three trigonometric functions of θ. 4 3 ? Pythagorean Theorem: (3)² + (4)² = c² 5 = c 5

21. BOOK ACTIVITY

22. Answer Try It 1 page 385

23. Answers: sin T = opp / hyp = 7/25 cos C = adj / hyp = 7/25 tan T = opp / adj = 7/24 sec C = hyp / adj = 25/7

24. Answer Try It 2 page 385

25. Answers: csc 45 = hyp / opp = square root of 2 sec 45 = hyp / adj = square root of 2 cot 45 = adj / opp = 1

26. Answer Try It 3 page 386

27. Answers: