Radians & The Unit Circle

When we discuss radians we are referring to the distance travelled along the track of the rollercoaster y 1 radian: when the distance travelled along the track is the same length as the radius Unit Circle center (0, 0) radius = 1 x 1

You go get a corndog. When you come back, the rollercoaster is stuck here… what might have happened?? Watch the rollercoaster & determine the radians

Converting Since in a full circle then dividing by 360 or dividing by 2 pi We can multiple anything by 1 and get an equivalent expression Used for converting to radians Used for converting to degrees

Convert to radians 1) 2)

Convert to Degrees 1) 2)

Positive & Negative Co-terminal Angles Remember when you went and got a corndog? It could have gone around once, twice, etc or even backwards! These are called Co-terminal Angles Positive- went counterclockwise & answer Positive Degrees- add 360 (until positive) Radians- add 2π (until positive) Negative- went clockwise & answer Negative Degrees- subtract 360 (until negative) Radians- subtract 2π (until negative)

Degrees 1) Positive Coterminal: Negative Coterminal: 2) Positive Coterminal: 410+360=770 Negative Coterminal: 410-360=50 50-360=-310 210+360= 570 210-360= -150 Still Positive!!!!

Radians 1) Positive: Negative:

You try 240 a) convert to radians b) positive Coterminal in radians c) negative Coterminal in radians 2) a) convert to degrees b) positive Coterminal in degrees c) negative Coterminal in degrees

1) 240 a) b) c) 2) a) 396 b) 756 or 36 c) -324

y We can label the x & y intercepts of the graph because the radius is one Since the top of the circle is one whole pi, we can count them out by 4ths This is (0, 1) This is (-1, 0) (1, 0) (0, 0) x 1 (0, -1) This is

Since the top of the circle is one whole pi, we can count them out by 6ths This is (0, 1) This is (-1, 0) (1, 0) (0, 0) 1 (0, -1) This is

Lets do all the radians at once… 6ths first- blue & green (ignore yellow!!!) (0, 1) Now the 4ths- yellow & green (ignore blue!!!) (-1, 0) (1, 0) (0, 0) 1 (0, -1)

Now you try and fill out the whole circle on your own (0, 1) (-1, 0) (1, 0) (0, 0) (0, -1)