Answer: (compiled from google)
One radian is the measure of the central angle of a circle such that the length of the arc is equal to the radius
of the circle.
A full revolution of a circle (
360
∘
) equals 2
π
r
a
di
a
n
s. This means that 1 radian
=
180
∘
π
.
The formula used to convert between radians and degrees is angle in degrees
=
angle in radians
⋅
180∘
π
.
The radian measure of an angle is the ratio of the length of the arc to the radius of the circle (
θ
=
sr
)
. In other words, if s is the length of an arc of a circle, and r is the radius of the circle, then the central angle containing that arc measures radians.
Key Terms
arc: A continuous part of the circumference of a circle.
circumference: The length of a line that bounds a circle.
radian: The standard unit used to measure angles in mathematics. The measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle.
The x
– and y
-coordinates at a point on the unit circle given by an angle
t are defined by the functions x
=
cos
t and y
=
sin
t
.
Although the tangent function is not indicated by the unit circle, we can apply the formula
tan t
=
sin t cos t to find the tangent of any angle identified.
Using the unit circle, we are able to apply trigonometric functions to any angle, including those greater than 90
∘
.
The unit circle demonstrates the periodicity of trigonometric functions by showing that they result in a repeated set of values at regular intervals.
Key Terms
periodicity: The quality of a function with a repeated set of values at regular intervals.
unit circle: A circle centered at the origin with radius 1.
quadrants: The four quarters of a coordinate plane, formed by the x
– and y
-axes.
If this doesn't help I appologize
