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Trigonometric Ratios

Trigonometric Ratios. SOH CAH TOA Nov. 16, 2018. The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions. SIN E. COS INE. TAN GENT. SIN E. Prounounced “sign”. COS INE. Prounounced “co-sign”. TAN GENT. Prounounced “tan-gent”.

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Trigonometric Ratios

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  1. Trigonometric Ratios SOH CAH TOA Nov. 16, 2018

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

  3. The Trigonometric Functions SINE COSINE TANGENT

  4. SINE Prounounced “sign”

  5. COSINE Prounounced “co-sign”

  6. TANGENT Prounounced “tan-gent”

  7. Greek Letter q Prounounced “theta” Represents an unknown angle

  8. hypotenuse hypotenuse opposite opposite adjacent adjacent

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

  10. Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment

  11. Sin SOHCAHTOA Opp Hyp Cos Adj Hyp Tan Opp Adj Old Hippie

  12. Finding sin, cos, and tan

  13. SOHCAHTOA Sin X = 10 8 6

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

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

  16. Find the sine, the cosine, and the tangent of angle A Give a fraction and decimal answer (round to 4 decimal places). B 24.5 8.2 A 23.1

  17. 1. 14 cm C 6 cm Finding an angle from a triangle To find a missing angle from a right-angled triangle we need to know two of the sides of the triangle. We can then choose the appropriate ratio, sin, cos or tan and use the calculator to identify the angle from the decimal value of the ratio. Find angle C • Identify/label the names of the sides. • b) Choose the ratio that contains BOTH of the letters.

  18. We have been given the adjacent and hypotenuse so we use COSINE: Cos A = Cos A = 1. Cos C = 14 cm C 6 cm H A Cos C = 0.4286 C = cos-1 (0.4286) C = 64.6o

  19. 2. Find angle x Given adj and opp need to use tan: Tan A = x 3 cm 8 cm Tan A = Tan x = A O Tan x = 2.6667 x = tan-1 (2.6667) x = 69.4o

  20. 3. Given opp and hyp need to use sin: Sin A = 12 cm 10 cm y sin A = sin x = sin x = 0.8333 x = sin-1 (0.8333) x = 56.4o

  21. Cos45 = Finding a side from a triangle To find a missing side from a right-angled triangle we need to know one angle and one other side. Note: If To leave x on its own we need to move the ÷ 13. It becomes a “times” when it moves. Cos45 x 13 = x

  22. We have been given the adj and hyp so we use COSINE: Cos A = 4. 7 cm 30o k Cos A = H A Cos 30 = Cos 30 x 7 = k 6.1 cm = k

  23. 5. We have been given the opp and adj so we use TAN: Tan A = 50o 4 cm r Tan A = A O Tan 50 = Tan 50 x 4 = r 4.8 cm = r

  24. 6. We have been given the opp and hyp so we use SINE: Sin A = 12 cm k 25o sin A = H O sin 25 = Sin 25 x 12 = k 5.1 cm = k

  25. 8. 7. 8 cm m x 25o 30o 5 cm Cos A = sin A = H Cos 30 = x = A x = 5.8 cm H sin 25 = O m = m = 18.9 cm

  26. Finding a side

  27. Ex. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle from his line of sight to the top of the tree as 71.5°. How tall is the tree? tan 71.5° ? tan 71.5° 71.5° y = 50 (tan 71.5°) 50 y = 50 (2.98868)

  28. Ex. 5 A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards

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