How to use this calculator

Changing a trigonometric function's scale, frequency, and shifts reveals its transformations. Sine and cosine have amplitude |A| and a period set by B. Tangent is unbounded and has vertical asymptotes instead of a finite amplitude. This graph breaks its curve at those asymptotes.

The method

y = A * trig(B(x-h)) + k

Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.

WORKED EXAMPLE

Function: Sine Vertical scale A: 1 Frequency factor B: 1 Horizontal shift h: 0 Vertical shift k: 0 x-axis angle unit: Radians Graph minimum x: -6.283185307 Graph maximum x: 6.283185307

Trigonometric graph: y = 1 sin(1(x - (0))) + (0)

The x-coordinate and horizontal shift are in radians.

Scope and limitations

The x-axis and horizontal shift use the selected angle unit. Up to 20 periods can be shown at once. Graphs are sampled views; they are not exact symbolic plots or general expression graphs.

Common questions

What happens when B is zero?

The trigonometric argument is fixed, so the visible function is constant wherever defined.

Why does tangent have gaps?

Tangent is undefined at its vertical asymptotes. Joining the curve across a gap would give a misleading plot.

References & further reading

External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.