Some Vocab!
 Initial side: starting position
of an angle.
 Terminal side: position after
rotation.
 Vertex: The endpoint of the
ray
 Central angle: vertex is at
the center of a circle.
Sketching Angles in
Standard Position
 An angle is in
standard position
if its vertex is
located at the
origin and its initial
side is on the xaxis.
 An angle is a
quadrantal angle
if the terminal side
of the angle lies
“on” one of the
axes.
Sketching Angles in Standard Position
FUN TIME!!
Sketching Angles in Standard Position
 Label
An angle in standard position if ______________________
_________________________________________________________________
_________________________________________________________________
An angle a quadrantal angle if ________________________
the quadrants.
 Label the arrows “Initial”
and “Terminal”
 Draw an arrow to show
how a positive angle will
rotate.
(counterclockwise)
An angle in standard position if ______________________
_________________________________________________________________
 Draw
an arrow to show
_________________________________________________________________
how a negative angle will
An angle a quadrantal
angle if ________________________
rotate.
(clockwise)
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
Coterminal
Angles
Definition
If 2 angles in standard
position have the same
terminal side, they are called
coterminal angles.
Coterminal in Degrees
 To find coterminal angles in
degrees, add/subtract multiples of
360°.
 45° 
 435° 
 −250° 
Coterminal in Radians
 To find coterminal angles in radians,
add/subtract multiples of 2π.
 −3π/2 
π 
 −5π/2 
Reference
Angles
Definition
 A reference angle is formed by
“dropping” a perpendicular from
the terminal side of a standard
position angle to the x-axis.
 Reference angles are always part
of the “bow tie”.
Because bow ties are cool.
Examples
Find the reference angle
for 208°
Find the reference angle
for 7π/4.
Finding Trig Ratios of
Ordered Pairs