Steps for graphing Tangent and Cotangent
Tangent:
Using the following basic Tangent function set-up: y = A tan( Bx + C )
1. Find two consecutive asymptotes by setting the variable expression in the tangent equal to −
solving :
Bx + C = −
π
2
and
Bx + C =
π
π
2
and
π
2
and
2
2. Find the x-intercept, midway between consecutive asymptotes.
3. Find the points on the graph midway between the x-intercept and the asymptotes. These points have ycoordinates of –A and A (from the coefficient of the tangent function).
NOTE: this function is increasing.
4. Steps 1-3 will produce one full period of the function. Add additional cycles to the left and right as needed.
Cotangent:
Using the following basic Tangent function set-up: y = A cot( Bx + C )
1. Find two consecutive asymptotes by setting the variable expression in the tangent equal to 0 and π and
solving :
Bx + C = 0
and
Bx + C = π
2. Find the x-intercept, midway between consecutive asymptotes.
3. Find the points on the graph midway between the x-intercept and the asymptotes. These points have ycoordinates of A and –A (from the coefficient of the cotangent function).
NOTE: this function is decreasing.
4. Steps 1-3 will produce one full period of the function. Add additional cycles to the left and right as needed.
Steps for graphing Secant and Cosecant
To graph the Secant and Cosecant functions:
1. Graph the reciprocal function (either “sine” or “cosine”)
2. Change all x-intercepts to vertical asymptotes.
3. Change all maximum points into minimum points, and all minimum points into maximum points.