sec. 5.1 angle measure - department of mathematics · november 05, 2011 problems • # 71 find the...
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Sec. 5.1 Angle Measure• Definition of RADIANS• If a circle of radius 1 is drawn with the vertex of the angle at its center, then the measure of this angle (in Radians) is the length of the arc that subtends the angle.
• Converting between degrees and Radians
Most common angles in degrees and radians
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Sec. 5.1 Angle Measure• Angles in Standard Position• Drawn with the vertex at the origin and the initial side on the xaxis.
• Two angles are “Coterminal Angles” if their sides coincide.
Sec. 5.1 Angle Measure• Length of Circular Arc
Arclength =
Angle (in radians) =
Radius =
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Problem: Suppose there is a circle of radius 5 feet. How many radians is 1/6 of the way around the circle?How many feet is 1/6 of the way around the circle?
Sec. 5.1 Angle Measure
• Area of a Circular Sector
Area of Sector =
Angle (in radians) =
Radius =
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Problem: Suppose there is a circle of radius 12 meters. How many radians is 1/3 of the way around the circle?Find the area swept out by going 1/3 of the way around the circle?
Sec. 5.1 Angle MeasureCircular Motion • Angular Speed
• Linear Speed
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Problems• #13 Find the degree measure equivalent to
• # 25 Give two positive angles and two negative angles that are coterminal with an angle of
Problems• # 43 Find an angle between 0 and that is coterminal with
• # 49 Find the length of the arc in the figure.
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Problems• # 71 Find the distance the earth travels in one day around the sun. The orbit of the earth is (almost) a circle of radius 93 million miles.
Sec. 5.1 Angle MeasureProblems• # 78 Suppose a ceiling fan has 16in blades and rotates at 45 rpm.
• Find the angular speed of the blade in radians per minute.
• Find the linear speed of the tips of the blade in feet per minute.
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Sec. 5.2 Trigonometry of Right Triangles
• Definition of six Trigonometric Ratios
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Sec. 5.2 Trigonometry of Right TrianglesProblems• # 3 Find the values of the six trig ratios
• # 5 Find the values of the six trig ratios
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Sec. 5.2 Trigonometry of Right Triangles• Values for Special Triangles
Consider a 454590 right triangle. Find the ratios of the sides.
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Sec. 5.2 Trigonometry of Right Triangles• Values for Special Triangles
Sec. 5.2 Trigonometry of Right Triangles• Values for Special Triangles
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Sec. 5.2 Trigonometry of Right TrianglesProblems• # 11 Find the length of the side labeled ‘x’.
• # 13 Find the length of the side labeled ‘x’.
Sec. 5.2 Trigonometry of Right TrianglesProblems• # 45 The angle of elevation to the top of the Empire State Building is 11 degrees from a distance of 1 mile from the base of the building. How tall is the building?
1,250 feet
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Sec. 5.2 Trigonometry of Right TrianglesProblems• # 55 A water tower is 325 feet from a building. From a window in the building you note that the angle up to the top of the tower is 39 degrees and down to the ground is 25 degrees. How tall is the water tower?
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