<p> Section 13-2 Angles and Angles Measures “Unit Circles”</p><p>(Start) Initial Side- (1/2 of the entire ray/angle) which is along the positive a-axis</p><p>(End) Terminal Side- Rotate around the center</p><p>Standard Position –Vertex is at the origin and initial side is on the positive x axis.</p><p>Remember your Quadrants??</p><p> Positive Angles go counterclockwise</p><p>Draw an angle with the given measure in standard position. 120° 120° = 90° + 30°. Draw the terminal side of the angle 30° counterclockwise past the positive y-axis.</p><p> You Try: Draw an angle of 225⁰</p><p> Negative angles go clockwise</p><p>–90° The angle is negative. Draw the terminal side of the angle 90° clockwise from the positive x-axis.</p><p> You Try: Draw an angle of -210⁰</p><p>Pictures/graphics from http://www.math.wfu.edu/Math105/basics%20of%20trigonometry.pdf and www.glencoe.com  Multiple angles go round and round (remember 360⁰ is one turn)</p><p>765° 765° = 360° + 360° + 45°. Draw the terminal side of the angle 45° counterclockwise past the positive x-axis. </p><p> You Try: Draw an angle of 495⁰</p><p>Converting to radians to degrees and vice versa</p><p>Degrees to radians-</p><p>260⁰ take degree and multiply by </p><p>So 260* = reduce to </p><p>Radians to degrees:</p><p>Radians to degrees—take the version and multiply by </p><p>So * = =</p><p>TRY THIS: Measure an Angle in Degrees and Radians ASTRONOMY- The Moon rotates on its axis about once every 27 Earth days. Find both the degree and radian measures of the angle through which it passes in 9 days. (Assume the rotation is counterclockwise.)</p><p>Coterminal angles</p><p>Coterminal angles -are angles that have the same end result of the graphs terminal position.</p><p>What does Means it works CO mean? together</p><p>Pictures/graphics from http://www.math.wfu.edu/Math105/basics%20of%20trigonometry.pdf and www.glencoe.com To find a coterminal angle add 360⁰ or subtract 360⁰ or any multiples of 360⁰</p><p>360⁰ Is the magic number!</p><p>Examples:</p><p> Find 3 coterminals of 240⁰</p><p>240 + 360 = 600⁰</p><p>240-360 = -120⁰</p><p>240+360+360 = 960⁰</p><p>The “RAD” Magic number!</p><p>Examples:</p><p> Give 2 other coterminals **Just carry the over to the answer.</p><p>+ 2 = </p><p>- 2=</p><p> Radians-“New Measurement” Measurement of an angle, Θ, in the standard position. Where the arc length is 1 unit on the unit circle.</p><p>The unit circle</p><p>Pictures/graphics from http://www.math.wfu.edu/Math105/basics%20of%20trigonometry.pdf and www.glencoe.com You need to memorize this for a quiz grade!</p><p>Pictures/graphics from http://www.math.wfu.edu/Math105/basics%20of%20trigonometry.pdf and www.glencoe.com </p>