Free · Trigonometry
Tangent Side Ratio and Angle Branches
Find tangent, an opposite or adjacent value, or a selected principal angle with full angular units.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
With opposite3 and adjacent4, tangent is0.75.
tangent = opposite/adjacent = tan(angle)
Worked example
Enter these known values and leave the other values blank.
- Opposite (a)
- 3
- Adjacent (b)
- 4
- Tangent
- 0.75
- Angle (α)
- 36.9 deg
Assumptions and limitations
- For a right triangle use positive leg lengths. Signed values may represent a general trigonometric ratio.
- Direct angle input covers zero through less than one full turn, excluding the two tangent poles. The inverse chooses one angle in [0,pi); adding pi gives the other full-turn solution.
Common questions
Why can tangent have two angles?
Tangent repeats every half turn. The inverse returns the representative from zero to less than pi radians.
Where is tangent undefined?
At90° and270°, cosine is zero. A zero adjacent denominator also has no finite ratio.
References
Remove the unused captured conditionangle JavaScript helper and express the tangent identity directly. Its inverse selects the angle in [0,pi), adding pi for negative tangent, while direct angles retain the captured full-turn domain. Correct the explanation label from cosine to tangent. Keep all ratio inverses and angular controls; require a nonzero adjacent-side denominator. Replace the external special-triangle illustration with original accessible definitions of opposite, adjacent and hypotenuse.