Unit circle
quadrant 1 coordinate signs
(+, +)
quadrant 4 coordinate signs
(+,−)
equation of unit circle
x² + y² = 1
Any point on the circle (x,y) represents
(cos∅, sin∅)
quadrant 2 coordinate signs
(−,+)
quadrant 3 coordinate signs
(−,−)
45 degrees on unit circle coordinate point
(√2/2, √2,2)
30 degrees on unit circle coordinate point
(√3/2, 1/2)
radian defintion
the unit of measure of a central angle that intercepts an arc equal in length to the radius of the circle
How do you find coterminal angles
you add or subtract 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Reference angle of quadrant "1" of unit circle
∅
Reference angle of quadrant "3" of unit circle
∅ -180
cos of 45 degrees
√2/2
sin of 45 degrees
√2/2
tan of 60 degrees
√3
cos of 30 degrees
√3/2
sin of 60 degrees
√3/2
tan of 30 degrees
√3/3
Quadrant "1" of unit circle what is positive
All
An angle is in standard position when
The vertex is at the origin and one side is on x axis
Reference angle defintion
a positive acute angle that is formed with he terminal side of an angle and the x- axis
Coterminal angle defintion
angles who share the same initial side and terminal sides they lie on top of each other.
left coordinate on unit circle
(-1,0)
bottom coordinate on unit circle
(0,-1)
top coordinate on unit circle
(0,1)
right coordinate on unit circle
(1,0)
60 degrees on unit circle coordinate point
(1/2, √3/2)
tan of 45 degrees
1
Sin of 30 degrees
1/2
cos of 60 degrees
1/2
Reference angle of quadrant "2" of unit circle
180- ∅
If the radius is 1 how many radians are in a full circle
2π
Reference angle of quadrant "4" of unit circle
360 - ∅
Coterminal angles drawn in standard position will always have measures that differ by an integer multiple of
360°
Quadrant "4" of unit circle what is positive
Cosine
Quadrant "2" of unit circle what is positive
Sin
0-360 degrees order of dots and starting point on unit circle
Starts on left dot 0, 30, 45, 60, 90 (top), 120, 135, 150, 180 (right), 210, 225, 240, 270 (bottom), 300, 315, 330, 360 (left dot)
Quadrant "3" of unit circle what is positive
Tan
How do we convert radians to degrees and degrees to radians
degrees/ 360 = radians/2π
what do u do to know quadrant numbers
draw a C and go 1234
Radius of unit circle
one unit
in which quadrant would the terminal ray of an angle drawn in standard position fall if the angle measures 860 degrees
quadrant 2
sec
reciprocal of cosine
csc
reciprocal of sin
cot
reciprocal of tangent
Negative angles are created by
rotating clockwise around the origin of a coordinate system, starting at the x-axis and proceeding through the quadrants
Positive angles are created by
rotating counter-clockwise around the origin of a coordinate system, starting at the x-axis and proceeding through the quadrants
