Free · Geometry and function relationships

Six Trigonometric Functions of an Angle

Use degree or radian units consistently. Reciprocal ratios are undefined when the corresponding sine or cosine is zero; principal inverse branches represent only one periodic solution.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For angle = 30, sin_print = 0.5, cos_print = 0.8660254037844386467637231707529361834714026269051903140279034895, sec_print = 1.154700538379251529018297561003914911295203502540253752037204653.

sin²(θ)+cos²(θ)=1; sec(θ)=1/cos(θ)

Worked example

Enter these known values and leave the other values blank.

Angle
30 deg
Result
Use degree or radian units consistently. Reciprocal ratios are undefined when the corresponding sine or cosine is zero; principal inverse branches represent only one periodic solution. Values: angle_degrees_print 30; sin_print 0.5; angle_degrees_print 30; cos_print 0.8660254037844386467637231707529361834714026269051903140279034898; angle_degrees_print 30; tan_print 0.5773502691896257645091487805019574556476017512701268760186023264; angle_degrees_print 30; cot_print 1.73205080756887729352744634150587236694280525381038062805580698; angle_degrees_print 30; sec_print 1.154700538379251529018297561003914911295203502540253752037204653; angle_degrees_print 30; csc_print 2;

Assumptions and limitations

  • Use degree or radian units consistently. Reciprocal ratios are undefined when the corresponding sine or cosine is zero; principal inverse branches represent only one periodic solution.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

Use degree or radian units consistently. Reciprocal ratios are undefined when the corresponding sine or cosine is zero; principal inverse branches represent only one periodic solution.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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