ANGLE MEASURES PREACALCULUS LESSON 2 – 1

STANDARD POSITION An angle is in STANDARD POSITION if the vertex is at the origin and the one ray is on the positive x-axis. 120 degrees -145 degrees

RADIANS The distance around a circle is 2π. Radians express the angle as a fraction of that 2π.

DRAW AN ANGLE 215 degrees -140 degrees 3π/4 degrees -π/6 degrees

CONVERTING FROM DEGREES TO RADIANS Radians are another way to measure angles and are based on the circumference of the circle. One π radian = 180 degrees Two π radians = 360 degrees To convert degrees to radians, multiply by To convert radians to degrees, multiply by

CONVERT THESE -30 degrees 5π 2 120 degrees -3π 8

COTERMINAL ANGLES Every rotation around the coordinate plane is 360 degrees or 2π radians. So to find a coterminal angle, add or subtract 360 or 2π till you have a normal angle.

FIND COTERMINAL ANGLES 390 degrees 780 degrees 8π/3 -12π/5

DEGREES, MINUTES, SECONDS To express an angle in a more precise way, you can use minutes and seconds appended to the degrees. 125o 38’ 125”