Sine= Opposite/Hypotenuse

Cosine= Adjacent/Hypotenuse

Tangent= Opposite/Adjacent

Opposite = the length of the side opposite θ
Adjacent = the length of the side adjacent to θ
Hypotenuse = the length of the hypotenuse

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Example of a Trigonometric Triangle


- Sine, Cosine, and Tangent can be used when finding side measurements of right triangles.
- When x and a side measurement are given, you can determine which formula you will use.

Sample Problems using above triangle:
1. What is the hypotenuse (H) measurement when x = 60° and O = 10in.?
  • sin(x) = O/H
    • sin(60°) = O/H
    • sin(60°) = 10in./H
    • H x sin(60°) = 10in.
    • H = 10in./sin(60°)
    • H = 11.55in.
2. What is the adjacent (A) measurement when x = 21° and H = 30ft.?
  • cos(x) = A/H
    • cos(21°) = A/H
    • cos(21°) = A/30ft.
    • 30ft. x cos(21°) = A
    • A = 28.00ft.
3. What is the opposite (O) measurement when x= 5° and A= 27cm.?
  • tan(x)= O/A
    • tan(5°) = O/A
    • tan(5°) = O/27cm.
    • 27cm. x tan(5°) = O
    • O = 2.36cm.



Special Triangles to Remember (These will make SOCAHTOA easier and faster to find) external image p6-5.gifexternal image a306090n.gif345.gif Fun Ways to Help Remember Sine, Cosine, and Tangent

  • the old Indian Chief: SOCAHTOA
  • oh heck, another hour of algebra!
  • oscar had a heap of apples

Sines, Cosines, and Tangents of Special Angles


sin 30˚ = sin π/6 = ½
sin 45˚ = sin π/4 = √2/2
sin 60˚ = sin π/3 = √3/2

cos 30˚ = cos π/6 = √3/2
cos 45˚ = cos π/4 = √2/2
cos 60˚ = cos π/3 = ½

tan 30˚ = tan π/6 = √3/3
tan 45˚ = tan π/4 = 1
tan 60˚ = tan π/3 = √3

Practice Problems:

righttriangle2.jpg

Use above triangle for practice problems.
Find the exact values of the six trigonometric functions for the triangle.



sin
cos
tan
csc
sec
cot
1. A = 0.6, B = 0.8, C = 1






2. A = 1, B = 1, C = √2, a = 45°, b = 45°






3. A = √3, B = 1, C = 2






4. A = 4, B = 3, C = 5






5. A = 6, B = 3






6. B = 2, C = 6