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1.1 Radian and Degree Measure.notebook Trigonometry: The study of triangles Unit 1 Lesson 1: Radian and Degree Measures In pre-calculus, we use the study of triangles to further our study on angles and circles. Important terms: Angle: determined by rotating a ray about its endpoint. Initial side: The starting ray Terminal side: The side that rotates about the fixed point Standard position: when the initial side of a ray coincides with the positive x-axis. What you should learn: What are radians and how do I convert between radians and degrees? How do I use angles to model and solve real-life problems? Why you should learn it: Radian measures are involved in numerous aspects of our daily lives including work with angles, trigonometry, calculus, architecture, and engineering. How many degrees would be in a total rotation (from the positive x-axis all the way back around)? y Positive angles: generated by counterclockwise rotation. How many degrees would be in half of a rotation? Negative angles: generated by clockwise rotation. A fourth? x y A sixth? An eighth? A twelfth? x 1.1 Radian and Degree Measure.notebook Radian Measure One radian is the measure of the central angle created when the arc length and radius are of equal length. One complete rotation in radians is II I units. So, 1/2 revolution = = 1/4 revolution = = ________ degrees ________ degrees 1/6 revolution = = ________ degrees III IV Coterminal Angles Converting from Degrees to Radians Two angles are coterminal when they have the same initial and terminal sides. angle, always subtract from the original angle. Ex. 0 and 2 To find a coterminal y If and Finding and Sketching Coterminal Angles Ex. Find the coterminal angle and sketch. x To convert degrees to radians, multiply degrees by To convert radians to degrees, multiply radians by Ex. Find the coterminal angle and sketch. Ex. Find the coterminal angle and sketch. ** For negative angles, ADD to find the coterminal angle! 1.1 Radian and Degree Measure.notebook Ex. Convert Degree Measures to Radians and Sketch. Ex. Convert from Radians to Degrees and sketch. y y a. 135 b. 540 a. x x b. c. -270 c. Complementary and Supplementary Angles You better remember what these are! (At least those of you that had me for geometry!!) Ex. Find the complement and supplement of each angle. a. 72 degrees b.148 degrees c. d.