Aim: How do we look at angles as rotation? Do Now: Draw the following angles: a) 60  b) 150  c) 225  HW: p.361 # 4,6,12,14,16,18,20,22,24,33

An angle is formed by joining the endpoints of two half-lines called rays. The side you measure from is called the initial side. Initial Side The side you measure to is called the terminal side. Terminal Side This is a counterclockwise rotation. This is a clockwise rotation. Angles measured counterclockwise are given a positive sign and angles measured clockwise are given a negative sign. Positive Angle Negative Angle

It’s Greek To Me! It is customary to use small letters in the Greek alphabet to symbolize angle measurement.       alpha betagamma theta phi delta The most used symbol is θ

We can determine the quadrant an angle is in by where its terminal side is in a standard position. Standard position: Vertex at (0,0) initial side is the positive x-axis. Use four different angles in all four quadrants to show that If then the angle is in Quadrant II If then the angle is in Quadrant III If then the angle is in Quadrant IV If then the angle is in Quadrant I

y x Initial side Angles at each quadrant on standard position Terminal sides

What happen if an angle is on the axis? We call the angle whose terminal side on either axis as quadrantal angles. Quadrantal angle is the angle whose degree measure is multiple of 90. For example etc., Example: Determine which quadrant is the angle in? a) 145  b) 240  c) 292  d) 75 

We call the angles that have the same terminal sides in a standard position as coterminal angles. If two angles are coterminal, the difference in their measures is 360º or a multiple of 360º For example: angle 80  is the same angle as – 280  80 – (-280) = 360 Find the coterminal angle of 150  150  – x  = 360 , x = – 210 

Determine the angles are coterminal or not: a)1630, 910 b) 5500, -170 c)1630, 50

If angle whose measure is greater than 360, how do we find the coterminal angle? Very simple: We just need to divide the angle by 360 , the remainder is the degree measure of the coterminal angle. For example: Find the smallest coterminal angle of 860  that is less than 360  and remainder is 140  therefore, the coterminal angle is 140  or -220 . Remainder is 140

Find the smallest coterminal angle less than 360 a)930  b) 1080  Determine which quadrant the angles locate a)170  b)350  c)-165  d)460  e)-210  210  00 II IV III II