Trigonometric Functions Calculator
Inputs
Result
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Related function values
For angle mode, these values use the same angle. For inverse mode, these show the selected inverse result converted into common angle units.
Formulas and assumptions
- Unit conversion: radians = degrees x pi / 180; gradians = degrees x 10 / 9; turns = degrees / 360.
- Core identities: tan(theta) = sin(theta) / cos(theta), cot(theta) = cos(theta) / sin(theta), sec(theta) = 1 / cos(theta), csc(theta) = 1 / sin(theta).
- Inverse ranges: arcsin returns [-90 degrees, 90 degrees], arccos returns [0 degrees, 180 degrees], and arctan returns (-90 degrees, 90 degrees). Arcsec and arccsc use arccos(1/x) and arcsin(1/x). Arccot returns atan(1/x), with arccot(0) = 90 degrees.
- Real-number limits: arcsin and arccos require -1 <= x <= 1. Arcsec and arccsc require |x| >= 1. Values very close to undefined points are treated as undefined to avoid misleading huge rounded numbers.
How to use this calculator
- Choose Angle to value for sin, cos, tan, csc, sec, or cot.
- Choose Value to angle for inverse trig functions such as arcsin or arctan.
- Enter the number, pick a unit and precision, then calculate. Use Copy or Download when you need to reuse the result.
Angles are normalized only for display context; the direct function calculation uses the entered angle after conversion to radians. That preserves values such as tan(450 degrees), which has the same tangent behavior as tan(90 degrees).
FAQs
Why does sin(30 degrees) equal 0.5?
On the unit circle, sine is the y-coordinate of the point at the given angle. At 30 degrees, that coordinate is exactly 1/2.
Why does the calculator say tan(90 degrees) is undefined?
Tangent divides sine by cosine. At 90 degrees, cosine is 0, so the division is undefined in real-number arithmetic.
Can I enter radians with pi?
This page accepts numeric input such as 1.57079632679. It does not parse symbolic expressions like pi/2, so use the degrees option or enter the decimal radian value.
Does this replace a triangle solver?
No. This calculator evaluates functions for one angle or one inverse input. To solve side and angle combinations, use the Trigonometric Triangle Solver.