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Unit 6 Day 1 December 12 th copyright2009merrydavidson Sit on your paper plate! Take markers, ruler, 1 pipe cleaner and protractor. Do not bend the pipe cleaner.
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OBJECTIVES TODAY both in degree and radian measure… 1.Terminology. 2.Sketch angles in standard position. 3.Sketch/find co-terminal angles. 4.Sketch/find reference angles. 5.Create the “unit circle”.
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4.1Angles An Angle is determined by the _________________ of a ray about its __________. The starting position of the ray is the _______________ side. The position after the rotation is the ________________ side.
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Initial side Terminal side You can not determine which is the initial or terminal side without showing the rotation
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An angle is in Standard Position angle if Initial side is along _______________ x - axis. Vertex is at the ____________
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The ___________________________ is determined by the amount of rotation from the ____________________ to the __________________.
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Standard Position & Quadrants positive x-axis origin 0o0o 90 o 180 o 270 o 360 o III IIIIV
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Paper Plate Unit Circles 1)Fold plate into quarters. 2)Draw in and label axes. 3)Label the quadrants. 4)Label +/- signs for each quadrant. 5)Using pencil, draw in the circle at the bend in the plate. (approx. 1 ½ inches from outside)
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Paper Plate Unit Circles 6)Label positive degree angles at 0, 90, 180, 270, 360 near the penciled in circle. 7)Using a protractor mark off and label angles of: 30 o, 45 o, 60 o, 120 o, 135 o, 150 o, 210 o, 225 o, 240 o, 300 o, 315 o, 330 o.
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If the rotation is counterclockwise the angle is ________________________. If the rotation is clockwise the angle is ___________________.
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Another way to measure angles is with _______________
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Radian Measure There are ____ radians in one complete revolution of a circle. Therefore…… 360 degrees = ____ radians
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Standard Position & Quadrants positive x-axis origin 0o0o 90 o 180 o 270 o 360 o III IIIIV
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Paper Plate Unit Circles Label the angles in radian measure.
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Co-Terminal Angles Co-terminal angles are angles in standard position that have the same _______________________________
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Find 1 positive and 1 negative angle Co-Terminal with the given angle. Add or subtract 360 o. 1) 40 o 2) -390 o 3) 137 o
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Find 1 positive and 1 negative angle Co-Terminal with the given angle. Add or subtract Be sure to get a common denominator with the radians. 4) 5) 6)
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Reference Angles Definition: For any angle (theta) that is in standard position, the reference angle… 1) Is acute 3) Has one side on the x-axis 4) Uses the terminal side of the given angle 2) Is positive
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Steps to draw the reference angle 1)Draw in the given angle w/ rotation 2)Connect the tip of the terminal side of the given angle to the x-axis. (mark it perpendicular to the x-axis) 3)The reference angle is the CENTRAL ANGLE formed by the right triangle.
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The PINK angle is the reference angle. From the x-axis to the terminal side of the given angle. Ref = given Ref = 180 - given Ref = 360 - given Ref = given - 180 These rules are for positive angles only!
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Sketch the given angle. Draw in the reference angle. Determine the measure of the reference angle. 7) 97 o 8) 192 o
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Sketch the given angle. Draw in the reference angle. Determine the measure of the reference angle. 9) 300 o 10)
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Paper Plate Unit Circles 8)Using a ruler, connect the origin to each of the angles you measured in quadrant I. 9)Put the pipe cleaner through the origin. Bend it in half. Twist the ends together.
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