Graph y = A·f(Bx + C) + D for all six trig functions with live parameter controls. See amplitude, period, phase shift, midline, max/min points, and asymptotes update in real time.
Parameters
Key Features
y = A · f(Bx + C) + D
A controls the amplitude (vertical stretch). |A| is the distance from midline to max/min. If A < 0, the graph reflects over the midline.
B controls the frequency. A larger |B| compresses the graph horizontally, making the period shorter.
C shifts the argument inside, producing a phase shift of −C/B. Positive result → shift right; negative → shift left.
D shifts every output value up or down, setting the vertical shift and the midline y = D.
Period = 2π / |B| (π / |B| for tan, cot)
Phase shift = −C / B
Midline: y = D
Amplitude = |A| (undefined for tan, cot, csc, sec — they have no bounded range).
Asymptotes appear for tan, cot, csc, and sec wherever the base function is undefined. Their positions shift with the phase shift.
Our Naruhodo tutors can walk you through amplitude, period, and phase shift with personalized examples — from graphing to verifying identities.