Transcript 12.2 Notes
Angles and Angle Measure 12.2 Warm up • Q: What is the greatest angle measure you recall seeing in Geometry? • Q: What do you think a negative angle measure might represent? Standard Position • An angle is in standard position when its initial side lies on the positive x-axis and its vertex is at the origin on a coordinate plane…. Measured counterclockwise from x-axis. Standard Position • • • • Initial side lies on pos. x-axis. Vertex centered at origin. Angle is on a coordinate plane. Terminal side (blue) here is in Quad III. • Red arc represents angle rotation. • Here the angle is positive since we see a counterclockwise rotation. Visualizing and drawing angles of rotation in standard position • Positive angle…negative angle. • Q: How would I show a 225o angle? • Q: In what quadrant does the terminal side lie? Draw this 225o angle. • Q: How would I show a -120o angle? • Q: In what quadrant does the terminal side lie? Draw this -120o angle. Example 1 • Draw an angle with the given measure in standard position. Then tell in which quadrant the terminal side lies. • (a) 215o (b) 400o (c) -90o • What would be a positive angle measure with the same standard position as -90o ? • How do you arrive at that measure? Coterminal Angle: • when two angles in standard position have terminal sides that coincide. **Find coterminal angles by adding or subtracting multiples of 360o from the original angle. Example 2 • Find one positive and one negative angle that are coterminal with: • a) -100o b) 575o Radians Conversions Example 3 • a) Convert 320 • b) Convert 5 12 to radians. radians to degrees. Example 3 • c) Convert -245 • d) Convert 3 4 to radians. radians to degree. Warm up Example 4 Draw the angle in standard position. Then find one positive and one negative coterminal angle. a) 2 𝜋 7 b) 8 − 𝜋 3 Arc Length - Central Angle – an angle with a vertex at the center of the circle. Example 5 • The steering wheel on a monster truck has a radius of 11 inches. How far does a point on the steering wheel travel if the wheel makes four fifths of a rotation? Example 6 • A carousel with a diameter of 25 ft. takes 16 sec. to make one rotation. If you ride the carousel for 2 minutes, how many feet does a point on the outer edge of the carousel revolve?