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Sin Cos Tan Calculator

With angle 30, sin cos tan comes to 0.500000 — sine. It is reached in 8 steps, the last of which is sin(0.5235988), and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Digital Library of Mathematical Functions §4.14, not an approximation fitted to it.

Sine, cosine and tangent of an angle in degrees or radians, with the angle also shown in the other unit and the reciprocal functions.

Formula and sources checked · How we check

Angle 30, Angle is in Degrees

0.500000

Sine for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

Sine
0.500000
Angle in radians
30 * pi / 1800.524
Angle in degrees
30 °
sin
sin(0.5235988)0.5
cos
cos(0.5235988)0.866
tan
sin(0.5235988) / cos(0.5235988)0.577
sec = 1/cos
1 / cos(0.5235988)1.155
csc = 1/sin
1 / sin(0.5235988)2
cot = cos/sin
cos(0.5235988) / sin(0.5235988)1.732

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Worked example

At 30 degrees the sine is exactly 0.5, the cosine is 0.8660254 (√3/2) and the tangent is 0.5773503 (1/√3). Those three are worth recognising on sight: they are the ratios of the 30-60-90 triangle, and a result that should be one of them and is not usually means the calculator was left in radians.

How to work it out yourself

  1. 1.Check the unit before the number. sin(30) is 0.5 in degrees and −0.9880 in radians, and nothing about the answer says which one you asked for.
  2. 2.The sine and cosine never leave −1 to 1. A value outside that range is an arithmetic slip, not a large angle.
  3. 3.The tangent has no value at 90 degrees and every 180 degrees after it. This calculator prints a dash there rather than the very large number floating-point arithmetic produces.

The formula

  1. Angle in radians30 * pi / 180
  2. Angle in degrees
  3. sinsin(0.5235988)
  4. coscos(0.5235988)
  5. tansin(0.5235988) / cos(0.5235988)
  6. sec = 1/cos1 / cos(0.5235988)
  7. csc = 1/sin1 / sin(0.5235988)
  8. cot = cos/sincos(0.5235988) / sin(0.5235988)

Source: NIST Digital Library of Mathematical Functions §4.14 — trigonometric functions, NIST DLMF §4.21 — addition and periodicity formulas

Questions people actually ask

Why does my calculator give a different answer for sin(30)?
It is in radians. 30 radians is roughly 1719 degrees, which lands at −0.988 rather than 0.5. Every scientific calculator has this mode and it is the single commonest cause of a wrong trigonometric answer.
What is a radian?
The angle that cuts an arc equal to the radius. A full turn is 2π radians, so one radian is about 57.2958 degrees. Radians are the unit calculus and physics use, because the derivative of sin x is cos x only when x is in radians.
Why is tan(90°) undefined rather than infinite?
The tangent is sin/cos, and at 90 degrees the cosine is zero. Approaching from below it grows without bound, from above it falls without bound, so there is no single value it approaches. Floating-point hardware returns about 1.6 × 10¹⁶ because π/2 is not exactly representable, which is an artefact of the binary, not a fact about the function.
Do the reciprocal functions have their own buttons?
Rarely. Secant, cosecant and cotangent are 1/cos, 1/sin and cos/sin, and most calculators expect you to take the reciprocal yourself. They are listed here because engineering and surveying formulas still quote them.

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