What are sin, cos and tan of 180 degrees?

Sine of 180° is 0, or 0.000000 as a decimal. Cosine is −1, which is -1.000000. Tangent is 0, or 0.000000. This angle sits on an axis rather than inside a quadrant, so its values are the extremes: exact integers and zeros rather than surds.

Why are csc and cot undefined at 180 degrees?

Because they are divisions and the denominator is exactly zero. Cosecant is 1 over sine, and sine of 180° is exactly 0. Cotangent is cosine over sine, so it divides by the same zero. Neither has a value — not a very large one, but none at all. The remaining functions are perfectly well behaved: sin 180° = 0.000000, cos 180° = -1.000000, tan 180° = 0.000000, sec 180° = -1.000000.

What is 180 degrees in radians?

180° is π radians, which is 3.141593 as a decimal, and 200.0000 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 180° is 50.0000% of a complete revolution.

Why does 180 degrees not belong to a quadrant?

Because it lies exactly on an axis rather than between two of them. The quadrants are the four open regions between the axes, and 180° points straight along one, so it belongs to none. These boundary angles are where the extreme values live — a sine or cosine of exactly 0, 1 or −1 — and where the functions that divide by them stop existing. Its reference angle is 0°.

How do the signs change from quadrant to quadrant?

They follow the coordinates. In the first quadrant both coordinates are positive so everything is positive. In the second the horizontal goes negative, so cosine, secant and tangent turn negative. In the third both are negative, so sine and cosine are negative but tangent — their ratio — comes back positive. In the fourth only the vertical is negative, so sine, cosecant and tangent are negative. The usual mnemonic, All, Sine, Tangent, Cosine, names the function that stays positive in each quadrant in turn.

What is a reference angle for?

It reduces every angle to a first-quadrant one. The reference angle is the acute angle between the terminal radius and the horizontal axis, always between 0° and 90°. Every trigonometric value of any angle equals the value of its reference angle with a sign supplied by the quadrant. Learn the first quadrant properly and the remaining three become sign bookkeeping rather than new material.

Why do some functions have no value at certain angles?

Because they are defined as divisions, and the denominator sometimes hits zero. Tangent and secant both divide by cosine, so both are undefined wherever cosine is zero — at 90° and 270°. Cosecant and cotangent divide by sine, so both are undefined where sine is zero — at 0°, 180° and 360°. Undefined does not mean very large. It means there is no such number, and a calculator reporting one is reporting its own rounding error.

Are radians better than degrees?

For calculation, yes, and it is not a matter of taste. The derivative of sine is cosine only when the angle is measured in radians; in degrees a factor of π/180 appears and never leaves. Every programming language expects radians for the same reason. Degrees survive because 360 divides neatly by so many numbers, which makes it convenient for navigation, construction and everyday description.

Do these values repeat?

Yes, and that periodicity is what makes trigonometry useful for anything that cycles. Sine and cosine repeat every 360°, so adding or subtracting whole turns changes nothing at all. Tangent repeats every 180°, half as far, which is why tan 60° and tan 240° are the same number. It follows that any angle, however large or negative, can be reduced to one between 0° and 360° before you do anything else.

Trigonometric Values of 180°

One hundred and eighty degrees is a straight angle — half a full turn — and the point has travelled all the way round to the far left of the unit circle, at coordinates (−1, 0). Cosine is therefore exactly −1, its most negative possible value, and sine is exactly 0. Tangent, sine over cosine, is 0 d...

ANGLE

UNIT

COMMON ANGLES

SIN 180°

0.000000

EXACT

180.0000° = 3.141593 rad = 200.0000 grad · on an axis · reference angle 0.00°

Created with❤️byeaglecalculator.com

HOW TO USE

1
This page opens with 180° already entered, so every value below is the answer for that angle — sine 0.000000, cosine -1.000000, and the rest — with no typing needed.
2
Read the exact form beside each decimal. At 180° the values are whole numbers and zeros rather than surds, because the angle lies on an axis.
3
Tap any of the six tiles to make it the headline figure. Note that csc and cot are marked undefined here — that is the correct answer, not a failure to compute.
4
Change the angle in the box, or press play, to turn this into the full trigonometry engine — right triangles and any triangle from SSS, SAS, ASA, AAS or SSA are all in the same tool.

THE FORMULAS

Sinesin A = opposite ÷ hypotenuse

Cosinecos A = adjacent ÷ hypotenuse

Tangenttan A = opposite ÷ adjacent

Reciprocalscsc = 1/sin · sec = 1/cos · cot = 1/tan

Pythagorean identitysin²θ + cos²θ = 1

Law of sinesa/sin A = b/sin B = c/sin C

Law of cosinesa² = b² + c² − 2bc·cos A

Area from two sidesarea = ½·a·b·sin C

Heron's formulaarea = √(s(s−a)(s−b)(s−c))

CircumradiusR = a ÷ (2·sin A)

Inradiusr = area ÷ s

Angle sumA + B + C = 180°

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

Sin Cos Tan of 90 Degrees

Calculate instantly →

Trigonometry Calculator

Calculate instantly →

Trig 90°

Calculate instantly →

Sin Cos Tan of 30 Degrees

Calculate instantly →

MORE TRIGONOMETRY CALCULATORS

Inverse Trig Calculator (arcsin arccos arctan)

Calculate instantly →

Sin Cos Tan Calculator

Calculate instantly →

Degrees to Radians Converter

Calculate instantly →

Sin Cos Tan of 0 Degrees

Calculate instantly →

Triangle Solver Calculator

Calculate instantly →

Sin Cos Tan of 60 Degrees

Calculate instantly →

Sin Cos Tan of 90 Degrees

Calculate instantly →

Sin Cos Tan of 360 Degrees

Calculate instantly →

Sin Cos Tan of 30 Degrees

Calculate instantly →

Sin Cos Tan of 180 Degrees

Calculate instantly →

Sin Cos Tan of 45 Degrees

Calculate instantly →

Sin Cos Tan of 270 Degrees

Calculate instantly →

Trig 60°

Calculate instantly →

Trigonometry Calculator

Calculate instantly →

Trig 0°

Calculate instantly →

Trig 30°

Calculate instantly →

Trig 90°

Calculate instantly →

Trig 120°

Calculate instantly →

Trig 150°

Calculate instantly →

Was this calculator helpful?

Last updated: July 29, 2026 · Formula verified · Every multiple of 15° is returned exactly, so tan 90° reads undefined rather than 1.6×10¹⁶ · Eagle-eyed accuracy for every calculation.