Below are the
graphs of the six
trigonometric
functions:
sine,
cosine,
tangent,
cosecant,
secant, and
cotangent. On the
$x$-axis are values of the
angle in radians,
and on the $y$-axis is
f (x), the value of the
function at each given angle.
Convince yourself that the graphs of the functions are correct. See that the
signs of the functions do indeed
correctly correspond with the signs diagrammed in the figure describing quadrant
signs in
Trigonometric
Functions, and
that the quadrantal angles follow the
rules described in the
quadrantal sign table.
Also, for example, consider the definition of sine. Given a point on the
terminal side of an angle, the sine of the angle
is the ratio of the
y-coordinate of that point to the distance between it and the origin. Now
imagine that angle changing, but the point remaining the same distance from the
origin. The point traces the circumference of a circle. As the angle goes from
0 to
radians, the
y coordinate increases, and so does the sine
of the angle. As the angle goes from
radians to
π radians,
the y-coordinate decreases, and so does the sine of the angle, but each is still positive. Then as
the terminal side of the angle enters the third and fourth quadrant, the
y coordinate
of the point on the terminal side is negative, and first decreases, and then
increases. All of these changes are indeed reflected in the graph. Below in the figure the quadrants of the
coordinate plane are represented in the graph.
