Transcript Sine and arc sine

SIDES OF A RIGHT ANGLE TRIANGLES
• A right angle triangle has 3 sides, and 2 sides are perpendicular
to each other
• The longest side of a right angle triangle is called the
hypotenuse.
Hypotenuse
SIDES OF A RIGHT ANGLE TRIANGLE
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Other than the hypotenuse, the other sides of a right angle triangle must
be made in reference to an angle:
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Consider the triangle below:
Opposite
y
Hypotenuse
Adjacent
Hypotenuse
x
Adjacent
Opposite
SINE
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There are 3 trigonometric functions: sine, cosine and tangent.
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In Physics, you will only need to use sine. (short form: sin)
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The Sine of an angle is defined as length of opposite side divided by
length of hypotenuse
Opposite
Hypotenuse
x
Adjacent
SINE
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For example, consider triangle below
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What is sin x?
4m
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•
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5m
x
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Opposite side = 4 m
Hypotheneus = 5 m
Recall: Sin x = opposite / hypotheneus
= 4/5
= 0.8 (no units!)
Note:
You can only Sine an angle
Trigo identities have no units
Sine and Cosine are always less than 1
ARC SINE
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Arc Sine is the opposite of Sine (sometimes called “inverse sine”)
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Symbol of Arc Sine is sin-1
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For Sine, I give you an angle, and you give me a ratio (i.e. length of opposite side
divided by hypotheneus)
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For Arc Sine, I give you the ratio, you give me the angle
4m
5m
x
Sin x = 0.8
Sin -1 (0.8) = x (in degrees)
[Can you find Sin-1 using your calculator?]
Sin -1 (0.8) = 53.1° (1 decimal place)
Note: this presentation is okay for Physics
exam, but is not allowed for Math exam!!
TEST YOURSELF
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Find Angle x using Arc Sine
6m
10 m
x
Sin x = 6/10 = 0.6
Sin -1 (0.6) = x
[Use calculator]
X = 36.9° (1 decimal place)