lecture2 - Chapter 1 Introduction.continued 1 Coordinate...

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Chapter 1 Introduction continued …continued 1
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Coordinate Systems Used to describe the position of a point in space Coordinate system consists of 1. A fixed reference point called the origin , O pecified directions or xes 2. Specified directions, or axes , a) scales ) bels b) labels 3. Instructions on how to label a point relative to the origin and the axes 2
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Cartesian coordinate system Also called rectangular axis label coordinate system x -and y -axes Points are labeled ( x,y ) rigin xis scale origin axis 3
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Different quadrants have y (m) different signs (+,+) (-,+) x (m) (-,-) (+,-) 4
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Log-log plot is a Cartesian coordinate system 1000 Log(y) 100 10 1 1 10 100 1000 Log(x) 5
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Plane polar coordinate system Origin and reference line are noted oint is located by Point is located by distance r from the origin in the direction of the angle , ccw from reference line Points are labeled ( r , ) 6
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Sign of the angle gives the direction to measure it r = 0 + - O 7
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Consider a right-angle triangle Hypotenuse Opposite side Adjacent side 8
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rigonometry Review Trigonometry Review pposite side sin opposite side hypotenuse djacent side  Hypotenuse Opposite cos adjacent side hypotenuse pposite side side tan oppos te s de adjacent side 9 Adjacent side
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More Trigonometry Pythagorean Theorem r 2 = x 2 + y 2 To find an angle, you need the inverse trig function i.e. , you know that sin = 0.707 What is the angle of your triangle? in - 707) = 45 = sin 1 (0.707) = 45° 10
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Degrees vs. Radians Be sure your calculator is set for e appropriate angular units for the appropriate angular units for the problem or example: For example: tan -1 0.5774 = 30.0° n - 5774 0 5236 rad tan 1 0.5774 = 0.5236 rad 11
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Rectangular Polar Rectangular to polar - given ( x, y ) use Pythagorean theorem to find r : r 2 = x 2 + y 2 use the inverse tangent to find angle: =tan -1 ( y / x ) Polar to rectangular - given ( r, ) os x = r cos y = r sin 12
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Problem 48 A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level round, she finds the angle to be 14.0° ground, she finds the angle to be 14.0 . a) Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. Hint: Use two triangles. ) elect variable names for the mountain height (suggestion: b) Select variable names for the mountain height (suggestion: y) and the woman’s original distance from the mountain (suggestion: x) and label the picture. ) sing the labeled picture and the tangent function write c) Using the labeled picture and the tangent function, write two trigonometric equations relating the two selected variables. ) ind the height y of the mountain by first solving one d) Find the height y of the mountain by first solving one equation for x and substituting the result into the other equation.
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This note was uploaded on 09/07/2009 for the course PHY 1603 taught by Professor Boudreaux during the Spring '08 term at The University of Texas at San Antonio- San Antonio.

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lecture2 - Chapter 1 Introduction.continued 1 Coordinate...

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