The Unit Circle is a circle with a radius of one unit about the origin.
(https://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%3D1)
The angle measures of the Unit Circle are measured in degrees and radians. For our purposes, we will stick to radians.
One revolution of the unit circle is
radians.On the Unit Circle, it is important to know what point value is located at certain radians.
The radians to know are
and 
.While each radian is associated with a unique point, there are only three points to know in order to know all of the values for the aforementioned radians, and those are the points in the x,y plane. This is because the rays that form the angles in radians of the x,y plane are reflections across axes. When you want to know the points in the -x,y plane, simply take the point of the complementary angle in the x,y plane and make the x-value a negative. When dealing with the -x,-y plane, make both values of the complementary angle's points negative. Finally, when working with the x,-y plane, make the y values of the complementary angles negative.
(www.gradeamathhelp.com)
With
and the Unit Circle, we can determine the values of the Trigonometric Functions.The Trig Functions are as follows:
Sine (sin) Cosecant (csc)
Cosine (cos) Secant (sec)
Tangent (tan) Cotangent (cot)
Each Trig Function has a unique relationship with the points and angles of the Unit Circle. Let
be a real number and let (x,y) be a point on the Unit Circle corresponding to 
.
As you may notice, the Trig Functions also have a relationship with each other. The Functions on the left and the functions on the right are reciprocals. The reciprocal relationships are between sin and csc, cos and sec, and tan and cot.
Note: When
, tan and sec are undefined. When 
, cot and csc are undefined.Remember that taking the trig function when
IS possible for all functions except for csc and cot.The domain of both sin and cos is
.The range of both sin and cos is
. This is because the radius of the Unit Circle is 1.Adding
to each value of 
in the interval 
completes a second revolution around the Unit Circle, thus 
and 
correspond to 
and 
. The same is true for repeated revolutions, whether they are positive or negative, which means:
for any integer n and real number
. This behavior is known as periodic.The Trig Functions, like any function, are defined as even or odd.
Even:
Odd:
ON A CALCULATOR be sure to set the mode from degrees to radians. ALSO there are no buttons for csc, sec, or cot. However, since these are the reciprocals of sin, cos, and tan, you can get by simply by dividing one by whichever function you need to produce the reciprocal, or by raising the function of the reciprocal to the negative first power.
Example:
or 
Good luck! <3 <3 <3
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