Turn sine expressions into cosine equations with steps. Review shifts, periods, tables, graphs, and exports using one clean responsive learning tool.
| Case | Sine Form | Cosine Form | Mode | Period |
|---|---|---|---|---|
| 1 | sin(x) | cos(x - π/2) | Radians | 2π |
| 2 | 2sin(3x + 1) | 2cos(3x + 1 - π/2) | Radians | 2π/3 |
| 3 | 5sin(2x + 30) - 4 | 5cos(2x - 60) - 4 | Degrees | 180 |
| 4 | -3sin(4x) | -3cos(4x - π/2) | Radians | π/2 |
The calculator uses the identity sin(θ) = cos(θ - π/2) in radians.
For degree mode, it uses sin(θ) = cos(θ - 90°).
If the function is y = A sin(Bx + C) + D, then the equivalent cosine form is y = A cos(Bx + C - π/2) + D.
The amplitude stays A. The frequency coefficient stays B. The vertical shift stays D. Only the phase term changes.
The period is 2π/|B| in radians and 360/|B| in degrees, provided B is not zero.
This calculator converts a sine function into an equivalent cosine function using a standard phase-shift identity. It helps students verify that both expressions produce the same y-values, even though the trig function name changes.
The tool displays the original sine form, the converted cosine form, the period, the adjusted phase, and a value table. It also plots both functions so you can confirm that the curves overlap across the selected interval.
Sine and cosine are the same wave shifted horizontally. A sine wave can be written as a cosine wave by subtracting a quarter-cycle from its angle. That quarter-cycle is π/2 in radians or 90 degrees in degree mode.
It is useful for school algebra, precalculus, trigonometry, engineering basics, and signal analysis practice. Teachers can also use it for examples because the conversion steps, data table, and graph are shown together on one page.
It converts a sine expression into an equivalent cosine expression. Both forms represent the same function after the angle is shifted by one quarter-cycle.
No. The amplitude remains the same. The conversion only changes the phase part inside the trig function.
Yes. The period depends on the frequency coefficient. Since that coefficient is unchanged, the period also remains unchanged.
Sine and cosine differ by a quarter-cycle. In radians, one quarter of 2π is π/2, so that shift converts sine to cosine.
In degrees, one full cycle is 360 degrees. One quarter of that cycle is 90 degrees, so the calculator subtracts 90 from the angle.
The trig input becomes constant, so the function becomes a constant value. In that case, the usual period is not defined.
The table verifies the identity numerically. Matching values show that the converted cosine expression is equivalent to the original sine expression.
Yes. You can download the computed table as CSV and export the visible result area as a PDF using the built-in button.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.