Radians and AnglesWelcome to Trigonometry!!

StarringThe Coterminal AnglesSupp & Comp AnglesThe ConverterAnd introducing

THE UNIT CIRCLEYou & I are gonna be great friends!

formed by rotating a ray about its endpoint (vertex)Starting positionEnding positionStandard PositionInitial side on positive x-axis and the vertex is on the origin

Angle describes the amount and direction of rotationPositive Angle- rotates counter-clockwise (CCW)Negative Angle- rotates clockwise (CW)

1 Radian = measure of central angle, , that intercepts the arc that has the same length as the radius of the circleArc length s = radius when = 1 radian

Calculate the number of radians in one full circle: C =03.140, 20, 6.28Therefore, we can say that 1 full revolution = 2 radians.

Coterminal Angles:Two angles with the same initial and terminal sidesFind a positive coterminal angle to 20Find a negative coterminal angle to 20

What did you find?These are just two possible answers. Rememberthere are more!

Complementary Angles: Two angles whose sum is 90Supplementary Angles: Two angles whose sum is 180

Convert to radians:

Convert to degrees:

1 degree = 60 minutes 1 = 60 1 minute = 60 seconds 1 = 60 So 1 degree = _________seconds 3600Express 365010as decimal degrees3636 +.8333 +.00277

ORUse your calculator!!Express 365010as decimal degrees

Enter 36Press this button Press enterEnter 50Press this button Go over to the symbol -- enterEnter 10Press this button Go over to the symbol -- enterPress enter

Convert 50 47 50 to decimal degree50.7972Convert 125 27 6 to decimal degree125.4517Can you go backwards and convert the decimal degree to degrees minutes seconds?Enter 125.4517 Go to DMS hit enter.

Express 50.525 in degrees, minutes, seconds50 + .525(60)

50 + 36.5

50 + 36 + .5(60) 50 degrees, 36 minutes, 30 seconds