Geom9point5and 6
Upcoming SlideShare
Loading in...5
×

Like this? Share it with your network

Share
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads

Views

Total Views
964
On Slideshare
964
From Embeds
0
Number of Embeds
0

Actions

Shares
Downloads
18
Comments
0
Likes
1

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 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
  • 20. Homework
    • Worksheets