Geom9point5and 6
- 1. Trig Basics & Beyond
- 2. Objectives Review of: Sin, Cos, Tan Learn Csc, Sec, Cot Learn inverse sin, cos, & tan Understand how to solve a right triangle
- 3. Sine Sine of A is: length of side opposite A a Length of hypotenuse c c a b A B C =
- 4. Cosine Cosine of A is: length of side adjacent to A b Length of hypotenuse c c a b A B C =
- 5. Tangent Tangent of A is: length of side opposite to A a Length of side adjacent to A b c a b A B C =
- 6. Shortcuts to Remembering Sin = opposite/hypotenuse Cos = adjacent/hypotenuse Tan = opposite/adjacent SOHCAHTOA
- 7. Practice SOHCAHTOA Sin = opposite/___________ Cos = _________/hypotenuse Tan = opposite/________
- 8. Practice – & reduce fractions Sin A 3/5 Cos A 4/5 Tan A ¾ Cos B 3/5 Sin B 4/5 Tan B 4/3 35 21 28 A B C SOHCAHTOA
- 9. Practice – & reduce fractions Sin B 12/13 Tan B 12/5 Cos A 12/13 Cos B 5/13 Sin A 5/13 Tan A 5/12 52 20 48 A B C SOHCAHTOA
- 10. Useful Stuff – Find a and b Sin A = opposite/hypotenuse = a/24 Sin 52 ◦ = a/24 .7880 = a/24 24*.7880 = 24*a/24 a = 18.912 24 a b 52 ◦ B C SOHCAHTOA
- 11. Solving Triangles – Find a and b Cos A = adjacent/hypotenuse = a/24 cos 52 ◦ = b/24 .6157 = b/24 24*.6157 = 24*b/24 b = 14.7768 24 a b 52 ◦ B C SOHCAHTOA
- 12. Inverse Sine If we know that the sine of angle A is .6691, then what is Angle A? We call this concept “inverse sine” It is written: sin -1 .6691 How do you do this on your calculator? 24 a b 52 ◦ B C
- 13. Solving Triangles – finding angles Sin A = opposite/hypotenuse Sin A = 5/12 Sin A = .4167 A = 25 degrees 12 5 b A B C SOHCAHTOA
- 14. Finding angles A + B + C = 180 degrees 25 + B + 90 = 180 B = 65 degrees 12 5 b A B C SOHCAHTOA
- 15. Another example – Find A, B, and x Tan A = opp/adj = 6/4 = 1.5 Tan 56 = 1.4826, tan 57 = 1.5399, so 56 degrees is closest to A B = 90 – A = 90 – 56 = 34 degrees X 2 = 4 2 + 6 2 X 2 = 52 X = 7.211 x 4 6 A B C SOHCAHTOA
- 16. Solving Triangles When the question asks you to “solve the triangle”, it means find all unknown sides and angles. For now, we are only solving RIGHT triangles. We’ll leave solving other triangles as something for you to look forward to . . .
- 17. What is a reciprocal? Two quantities are a pair of reciprocals if their product is +1 8 and 1/8 are a pair of reciprocals What is the reciprocal of 3/2?
- 18. Definitions of Cosecant, Secant, and Cotangent Sine is a reciprocal of cosecant Sine = opp/hyp Cosecant = Csc = hyp/opp Cosine is a reciprocal of secant Secant = sec = 1/cos = hyp/adj Tangent is a reciprocal of cotangent Cotangent = cot = adj/opp
- 19. csc A 5/3 sec A 5/4 cot A 4/3 sec B 5/3 cot B 3/4 csc B 5/4 Practice – & reduce fractions 35 21 28 A B C