Reciprocal trig transformations • visual math studio

See how secant, cosecant, and cotangent transform.

Adjust the vertical stretch, frequency, phase shift, and vertical shift, then compare the transformed graph to the parent reciprocal trig function. Use presets for quick examples, quiz mode for practice, or type your own values like a student solving homework.

Secant, cosecant, cotangent

Live graph + equation

Quiz mode

Teacher demo mode

Current transformation

Period / spacing

Shift summary

Quick examples

Jump into a classic parent graph, a stretch, or a shifted reciprocal trig function.

Choose the reciprocal trig function

Use sliders for intuition, then switch to student input mode to type your own values for A, B, h, and k for secant, cosecant, or cotangent.

Amplitude / vertical stretch (A)

Negative values reflect the graph across the x-axis.

Frequency / horizontal scale (B)

Changing B changes the period. Negative values reflect across the y-axis before shifting.

Phase shift (h)

Positive h moves the graph to the right in the form y = A f(B(x - h)) + k.

Vertical shift (k)

Moves the midline up or down.

Graph helpers

Blue dots mark transformed reference points. Pink dashed lines show reciprocal trig asymptotes.

Key points shown

Live graph

Parent function shown in gold. Transformed graph shown in blue.

Compare with parent graph

Transformed function Parent function Axes + grid Midline Asymptotes / key points

Amplitude / vertical stretch

Period and spacing

Phase shift

Vertical shift

Quiz mode

Press New quiz to identify a transformation from the graph.

Function Amplitude A Frequency B Phase shift h Vertical shift k

Teacher demo mode

Use the scripted steps below to walk through transformations in a clean order.