Your result
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Enter your values, then click Calculate result.How this calculator helps
Calculate sine, cosine, tangent and principal inverse angles with an explicit degree or radian setting and domain checks. For sine, cosine and tangent, enter an angle in the selected unit. For inverse sine, inverse cosine and inverse tangent, enter a dimensionless ratio; the unit setting then determines the output angle. The same value 30 means very different angles in degrees and radians. A ratio of 0.5 is neither 0.5 degrees nor half a turn, so choose the function before interpreting the number.
How to use it
- 1
Select the correct input roles for trigonometric functions calculator and enter the values described below. The demonstration defaults illustrate the method; they are not independently verified personal measurements or live market data.
- 2
Review principal inverse ranges and the original source record. Match units, signs and the chosen mode before submitting, rather than relying on a familiar-looking default number.
- 3
Click Calculate result to submit the current fields. Editing an input preserves the prior submitted output until you calculate again; the pending-change message distinguishes that saved output from the new values.
- 4
Check the labeled output against the worked example and independent verification steps. Review scope and precision before using the result in another document, and keep the complete input basis with a copied answer.
Formula and methodology
Degrees × π/180 = radians. Forward functions evaluate sin θ, cos θ or tan θ. Inverse functions return their principal real angle.
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
Sine of 30 degrees equals 0.5. Choose inverse sine, enter ratio 0.5 and select degrees to recover the principal angle 30 degrees. In radians that inverse result is π/6, approximately 0.523598776. Inverse sine does not return every angle with sine 0.5; 150 degrees is another forward solution outside its principal range.
How to interpret your result
Sine and cosine ratios must lie between −1 and 1 before their real inverses can be evaluated. Inverse tangent accepts any supported finite ratio. Tangent is undefined when cosine is zero, including odd multiples of 90 degrees. Values with a computed cosine magnitude below 10⁻¹² are rejected as too close to that singularity; the browser cannot reliably display an arbitrarily large near-pole value.
For different inputs or formulas, use Right Triangle Calculator; Logarithm Calculator; Slope Calculator.
Related questions this calculator covers
- calculator with inverse functions
- tan inverse calculator
- cosine calculator
- sin cos and tan calculator
- cos calculator
- calculator trigonometri
Scenario comparison
| Scenario | What it shows |
|---|---|
| Zero angle | sine and tangent are zero, while cosine is one. |
| Unit equivalence | sine of 180 degrees agrees with sine of π radians within rounding. |
| Principal branch | inverse sine of −1 gives −90 degrees. |
Common mistakes to avoid
- Confusing reciprocal notation with inverse function notation.
- Treating a forward angle as an inverse ratio.
- Expecting one principal inverse angle to describe every equation solution.
Compute sine and cosine of the same modest angle and check their squared sum. Convert the angle independently to radians and repeat. For an inverse result, apply the corresponding forward function and compare with the entered ratio. Repeated rotations should preserve forward values, although rounded large angles can lose precision.
Authoritative reference. Method and scope reviewed on 5 October 2026. SolvePilot provides the original worked example and bounded browser implementation. Editorial and arithmetic review by Mohammad Qasim does not certify user measurements, a real contract or an individual professional decision. The reference supplies method, unit or source-record context; it does not approve this implementation or its inputs.What can affect the result?
Angle or ratio
For sine, cosine and tangent, enter an angle in the selected unit. For inverse sine, inverse cosine and inverse tangent, enter a dimensionless ratio; the unit setting then determines the output angle. The same value 30 means very different angles in degrees and radians. A ratio of 0.5 is neither 0.5 degrees nor half a turn, so choose the function before interpreting the number.
Principal inverse ranges
Inverse sine returns angles from −90 to 90 degrees, inverse cosine from 0 to 180 degrees, and inverse tangent strictly between −90 and 90 degrees. These are principal branches chosen to make each inverse single valued. A trigonometric equation can have other solutions after symmetry and full rotations are considered. This page evaluates one numeric function rather than solving a complete equation or generating its general solution.
Domain and singularities
Sine and cosine ratios must lie between −1 and 1 before their real inverses can be evaluated. Inverse tangent accepts any supported finite ratio. Tangent is undefined when cosine is zero, including odd multiples of 90 degrees. Values with a computed cosine magnitude below 10⁻¹² are rejected as too close to that singularity; the browser cannot reliably display an arbitrarily large near-pole value.
Useful numerical checks
Sine squared plus cosine squared should be approximately one for the same angle. Tangent should agree with sine divided by cosine away from its poles. To compare degrees and radians, multiply a degree input by π/180 and retain sufficient digits. Rounding the converted angle before evaluating can shift the last displayed decimals, especially near a steep part of the tangent curve.
Scope and precision
Inputs are bounded to magnitudes no greater than one million, and the arithmetic uses browser floating point. This is a numeric trigonometry worksheet, not a general scientific-expression parser, symbolic identity prover or physics simulator. Do not enter expressions such as π/6; use their numeric radian value. Results do not establish surveying or engineering tolerance. Keep the function, angle unit and original input with any copied answer.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
Inputs are bounded to magnitudes no greater than one million, and the arithmetic uses browser floating point. This is a numeric trigonometry worksheet, not a general scientific-expression parser, symbolic identity prover or physics simulator. Do not enter expressions such as π/6; use their numeric radian value. Results do not establish surveying or engineering tolerance. Keep the function, angle unit and original input with any copied answer.
Sources and review information
Frequently asked questions
What does inverse sine mean?＋
It returns the principal angle whose sine matches your supplied ratio. It does not mean one divided by sine, and it does not list every periodic solution.
Why can tangent fail at 90 degrees?＋
Cosine is zero there, so sine divided by cosine is undefined. A tiny numerical cosine is treated as a pole instead of producing misleading finite precision.
Can I enter pi divided by six?＋
The numeric field does not parse expressions. Enter approximately 0.523598775598299 and choose radians, or use 30 with degrees.
Can inverse cosine use 2?＋
No real angle has cosine 2. The accepted ratio range for inverse sine and inverse cosine is −1 through 1.
Does this solve triangles?＋
It evaluates individual functions. Triangle side and angle solving belongs to the separate right-triangle worksheet with its own geometric inputs.