Explore angles in standard position, coterminal angles using an HTML 5 applet. Example: Sketch each angle in standard position. Draw Angles - Plotting Program. You can draw an angle in standard position by positioning its vertex at the origin and one "ray" on the positive x-axis. Explained below. Add +360 degrees until you have a positive angle, then sketch. Standard Position: An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The reference angle is the acute angle which this line OP makes with the x- axis. One revolution is equivalent to the circumference C = 2πr. 510° 4. 1. 270° 3. Consider the angle θ = –150°. The position of the first arm remains, the second arm rotates counter-clockwise at increasing angle. If the terminal side of an angle lies "on" the axes (such as 0º, 90º, 180º, 270º, 360º ), it is called a quadrantal angle. (c) Convert the angle to radian measure. Since the given angle is negative, we need to measure in the clockwise direction.. It makes sense here to state the angle in terms of its positive coterminal angle. (e) Find the exact values of the six trigonometric functions of θ. 150° 2. You start with the x - and y -axes, which cross at a right (90°) angle. The ray on the x-axis is called the initial side and the other ray is called the terminal side. (b) Determine a coterminal angle in the interval [0°, 360°). The ray on the x-axis is called the initial side and the other ray is called the terminal side.. The angle of 240^o is drawn as shown in the figure. The reference angle is the angle from the sketch to the x-axis, in this case, 60 degrees. This angle would measure 60^o as shown in the figure . Angle of 0^o is taken to be along the positive x-axis. -240+360=120 Since 120 is positive, you can stop here. Answers to Drawing Angles in Standard Position 1) x y 2) x y 3) x y 4) x y 5) x y 6) x y 7) x y 8) x y 9) x y 10) x y 11) x y 12) x y 13) x y 14) x y 15) x y 16) x y 17) x y 18) x y 19) x y 20) x y. –720° (II) Angles measured in Degrees and Radians Degree Measure Radian Measure What is radian measure? Reference angle is the acute angle between the terminal side of the given angle and the horizontal axis.. It is indicated along the line OP in the figure. (a) Sketch the angle in standard position. Standard position means that the positive x axis (the horizontal axis, and to the right hand side) is 0 degrees, and we rotate in the counter-clockwise directions. –210° 5. Since #color(red)(theta = (-160^@)#, we must determine the Coterminal angle. Plotting program for angles. Then turn anti-clockwise by 240 degrees to draw the angle as desired. (d) Find the reference angle θ′. To find this, add a positive rotation (360 degrees) until you get a positive angle. It depends on the Quadrant the given angle belongs to, in degrees.. We will sketch the given angle in standard position.. Title: Drawing Angles in Standard Position Author: Tess Created Date: Let's try our hand at drawing an angle in standard position measured in degrees. If we consider the unit circle Angles in Standard Position Remember, there are 360° in a full circle.
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