The sine function, is one of the three main trigonometry
functions. The sine of the angle theta is the
ratio of the opposite side
over the hypotenuse. This ratio is the same on any
size circle. On the unit circle
the hypotenuse is equal to one, so the sine value is always equal to y
variable using trigonometric conventions.
The sine function is the reciprocal function of the
cosecant function. The sine of 0 degrees
is equal to zero. As the theta
angle goes up from 0 degrees to 90 degrees the value of the sine moves from
zero up to one in the first quadrant of the coordinate
system of the Cartesian Plane. As the theta
angle hits 90 degrees the value of the sine reaches one. The angle then extends
into the second quadrant and the value of the sine starts decreasing. As the
theta angle goes through 180 degrees it reaches
zero again then enters the third quadrant. Here the value is negative because
the y variable is negative. The hypotenuse is
always positive, remaining equal to one. Starting at 180 degrees the value
decreases and finally is equal to negative one at an angle equal to 270 degrees.
As the theta angle enters the fourth quadrant
the value of the sine moves from a low of negative one and increases to reach
zero again at 360 degrees. Any angle beyond 360 degrees, which is a full circle,
repeats the cycle. The domain of the sine function
is the set of real number. It represents the angle
input into the function and can be expressed in degrees or radians.
The range of the sine function is limited from negative
one to positive one.
Sine function:
Sine (0 degrees) = 0,
Sine (30 degrees) = .5,
Sine (45 degrees) = .71,
Sine (60 degrees) = .87,
Sine (90 degrees) = 1,
Sine (135 degrees) = .71,
Sine (180 degrees) = 0,
Sine (210 degrees) = -.5,
Sine (240 degrees) = -.71,
Sine (270 degrees) = -1,
Sine (315 degrees) = -.71,
Sine (330 degrees) = -.5,
Sine (360 degrees) = 0.