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7.5 & 7.6– Apply the Sin-Cos-Tan Ratios

7.5 & 7.6– Apply the Sin-Cos-Tan Ratios. Side opposite the given angle. Side opposite the right angle. Side touching the given angle, but not the hypotenuse. A. c. b. C. a. B. sin. tan. cos. opp hyp. adj hyp. opp adj. sin A ° =. cos A ° =. tan A ° =. a c. b c. a b.

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7.5 & 7.6– Apply the Sin-Cos-Tan Ratios

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  1. 7.5 & 7.6– Apply the Sin-Cos-Tan Ratios

  2. Side opposite the given angle Side opposite the right angle Side touching the given angle, but not the hypotenuse

  3. A c b C a B sin tan cos opp hyp adj hyp opp adj sin A° = cos A° = tan A° = a c b c a b sin A° = cos A° = tan A° = S O H C A H T O A

  4. Note: You cannot use trig ratios on the right angle

  5. 1. Find the sin R and sin S. Write your answer as a fraction. SOH – CAH – TOA 15 17 sin R° = 8 . 17 sin S° =

  6. 2. Find the cos A and cos B. Write your answer as a fraction. SOH – CAH – TOA 16 20 cos A° = 12. 20 cos B° =

  7. 3. Find the tan A and tan B. Write your answer as a fraction. SOH – CAH – TOA 10 24 tan A° = 24. 10 tan B° =

  8. 4. Write the trigonometric ratio as a decimal to two decimal places. a. sin 62° b. cos 25° c. tan 38° 0.78 0.88 0.91

  9. 5. Solve for x. Round to two decimal places. 1 x  tan35° = 4 tan35° tan35° 5.71 x =

  10. When solving for a triangle using trigonometry, ask yourself these questions: 1. 2. 3. 4. What acute angle do I know? What side do I know? What side am I solving for? What is the relationship between the angle I know and the two sides? (opp, adj, or hyp)

  11. 6. Approximate the missing variables to two decimal places. SOH – CAH – TOA A O H H a b a. 10 b. 10 cos 50° = sin 50° = 1 1 10  cos 50° = a 10  sin 50° = b 6.43 = a 7.66 = b

  12. 6. Approximate the missing variables to two decimal places. SOH – CAH – TOA O H A H c d c. 7 d. 7 sin 42° = cos 42° = 1 1 7  sin 42° = c 7  cos 42° = d 4.68 = c 5.20 = d

  13. 7. Approximate the missing variables to two decimal places. SOH – CAH – TOA O O A H m n 25 m 25 n tan 39° = sin 39° = 1 1 m tan 39° = 25 n sin 39° = 25 tan 39° tan 39° sin 39° sin 39° m = 30.87 n = 39.73

  14. 7. Approximate the missing variables to two decimal places. SOH – CAH – TOA O A H H t u t. 32 u. 32 sin 51° = cos 51° = 1 1 32  sin 51° = t 32  cos 51° = u 24.87 = t 20.14 = u

  15. 7. Approximate the missing variables to two decimal places. SOH – CAH – TOA O O A H a b 14 a 14 b tan 57° = sin 57° = 1 1 a tan 57° = 14 b sin 57° = 14 tan 57° tan 57° sin 57° sin 57° a = 9.09 b = 16.69

  16. 7. Approximate the missing variables to two decimal places. SOH – CAH – TOA A O H A m n 79 m n . 79 cos 31° = tan 31° = 1 1 m cos 31° = 79 79  tan 31° = n cos 31° cos 31° n = 47.47 m = 92.16

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