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# Geom9point5and 6

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• 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
• 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
• = 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
• 20. Homework
• Worksheets