Working with Angles in Standard Position: Understanding Unit Circle
Explore angles in standard position and their relationships within the unit circle. Review concepts of special right triangles, coterminal angles, and reference angles. Practice identifying angle measures and determining coterminal angles within specified ranges.
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Presentation Transcript
Angles & the Unit Circle Day 1 Today s Objective: I can work with angles in standard position.
Review: Special Right Triangles 30o 45o 2 s 2 s 3 s s 45o 60o s s
The blue arrow is fixed to the x-axis. Turn the red arrow counterclockwise about the origin. If the red arrow contains one of the points when it stops, which point would create the angle with the greatest measure? Explain your reasoning (0, 1), (2, 2), (-3, 3), (-1, 0), or (5, 5) Angle on coordinate plane in standard position: Terminal side Initial side + 1. 2. Vertex on origin One ray of angle is on positive x-axis Reference Angle
What are the measures of each angle? What is the reference angle? 90 90 120 ( 2,2 3) 60 45 ( 2, 2) 135 Sketch each angle in standard position. 85 What is the reference angle? 320 85 40
Coterminal angles angles that have the same terminal side Which angles are coterminal? A300 B 60 C60 D 420 Which coterminal angle is between 0 and 360 ?300 495 = 135 + 360 135 225 Pg. 835 #1-7 odd Pg. 840 #7-25 odd Which angles are coterminal? A 315 B45 C315 D405 Which coterminal angle is between 0 and 360 ? 45
