Aim: How do we look at angles as rotation? Do Now: Draw the following angles: a) 60 b) 150 c) 225  

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

      It’s Greek To Me! The most used symbol is θ alpha beta It is customary to use small letters in the Greek alphabet to symbolize angle measurement.    alpha beta gamma    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 I If then the angle is in Quadrant II If then the angle is in Quadrant III If then the angle is in Quadrant IV

Terminal sides Angles at each quadrant on standard position y Initial side x 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: 1630, 910 5500, -170 1630, 50

Very simple: We just need to divide the angle by 360 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 . Remainder is 140 and remainder is 140therefore, the coterminal angle is 140or -220

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

Another unit to measure angle is the radian Degree Vs Radian To measure an angle we can another unit besides degree Another unit to measure angle is the radian Radian is the central angle that intercepts an arc whose length is the same as the radius.

O  r = 1 1 radian Arc length = 1 The circle has radius equals 1. The central of the circle that intercepts the arc with length 1 is equal to 1 radian Use the same reason, if the radius is 2 units then the central angle equals 1 radian when the intercepted arc is also 2 units

One circle = 360° (degrees) One circle = 2π radians ----------------------------------- 1π radians = 180° 90  /2 radians 270  3/2 radians

The rules for conversion of degree & radian Degree to radian Radian to degree Convert 75 to radian in terms of  36 Convert to degree

Convert into degree 1. 18 2. 72 3. 135 4. 330

Convert into radian 1. 240 2. 200 3. -396 4. 500