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Trigonometry: The study of triangles (sides and angles)

astronomy. geography. engineering. The Primary Trigonometric Ratios. Trigonometry: The study of triangles (sides and angles). Trigonometry has been used for centuries in the study of:. surveying. physics. Parts of a Right Triangle. B. hypotenuse. opposite. A. C. adjacent. B.

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Trigonometry: The study of triangles (sides and angles)

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  1. astronomy geography engineering The Primary Trigonometric Ratios Trigonometry: The study of triangles (sides and angles) Trigonometry has been used for centuries in the study of: surveying physics

  2. Parts of a Right Triangle B hypotenuse opposite A C adjacent

  3. B hypotenuse adjacent C opposite A

  4. B hypotenuse opposite A C adjacent

  5. B hypotenuse adjacent C opposite A

  6. B hyp opp C A adj TOA SOH CAH

  7. B SOH CAH TOA hyp 10 opp 8 A C 6 adj

  8. B hyp SOH CAH TOA 5 adj 3 A C 4 opp

  9. SOH CAH TOA B hyp 13 5 adj A 12 C opp

  10. Use a calculator to determine the following ratios. 0.3584 sin 21° = cos 53° = 0.6018 tan 72° = 3.0777

  11. Determine the following angles(nearest degree). sin A = 0.4142 ÐA = sin-1(0.4142) = 24° ÐB=cos-1(0.6820) cos B = 0.6820 = 47° ÐC =tan-1(1.562) tan C = 1.562 = 57°

  12. Determine the following angles(nearest degree). sin A = ÐA = sin-1(0.5833) = 36° = 0.5833 cos B = ÐB = cos-1(0.2666) = 75° = 0.2666 ÐC = tan-1(1.875) tan C = = 62° = 1.875

  13. B Example 1: Determine side a opp hyp SOH CAH TOA 6 cm a 30º A C a = 6 sin 30° a = 6 (0.5) a = 3 cm

  14. Ex. 2: Name two trig ratios that will allow us to calculate side b. B 50º 9 m 40º b A C

  15. Example 3: Determine side b B SOH CAH TOA 55º 8 cm adj b C A opp b=8 tan 55° b= 8 (1.428) b= 11.4 cm

  16. Example 4:Determine the measure of ÐP. SOH CAH TOA R adjacent cos P = 0.70588 12 cm ÐP = cos–1(0.70588) Q 17 cm ÐP = 45.1° P hypotenuse

  17. Example 5:Determine the measure of side PR. Method 1 adj opp R q 12 cm q(tan 35°) = 12 35° P Q q= 17.1cm

  18. Example 6:Determine the measure of side PR. Method 2 adj opp R ÐQ = 90°– 35° q ÐQ = 55° 12 cm 35° 55° P Q q= 12(tan 55°) q= 12(1.428) q= 17.1cm

  19. R Q P Ex. 7:In DPQR, ÐQ = 90°. a) Find sin R if PR = 8 cm and PQ = 4 cm. 8 cm b) Find cos R . 4 cm RQ2 = 82 – 42 RQ2 = 64 – 16 RQ2 = 48

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