What are sin, cos and tan of 360 degrees?

Sine of 360° 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 360 degrees?

Because they are divisions and the denominator is exactly zero. Cosecant is 1 over sine, and sine of 360° 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 360° = 0.000000, cos 360° = 1.000000, tan 360° = 0.000000, sec 360° = 1.000000.

What is 360 degrees in radians?

360° is 2π radians, which is 6.283185 as a decimal, and 400.0000 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 360° is 100.0000% of a complete revolution.

Why does 360 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 360° 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°.

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.

What are cosecant, secant and cotangent for?

They are the reciprocals — cosecant is 1/sine, secant is 1/cosine, cotangent is 1/tangent — and they exist because certain formulas are far tidier written with them. The derivative of tangent is secant squared, which is much neater than the alternative. In practice you will meet them most often in calculus and in engineering conventions rather than in triangle work, where the main three do everything.

How do I get an exact value rather than a decimal?

Recognise the angle first. If it is a multiple of 30° or 45°, the value is one of a small set: 0, 1/2, √2/2, √3/2 and 1 for sine, the same list reversed for cosine, and 0, √3/3, 1, √3 for tangent. Take the magnitude from the reference angle and the sign from the quadrant. Writing sine as √0/2, √1/2, √2/2, √3/2, √4/2 across 0°, 30°, 45°, 60° and 90° makes the pattern hard to forget.

Trigonometric Values of 360°

Three hundred and sixty degrees is a complete revolution, and every value here is identical to the value at 0° — cosine exactly 1, sine exactly 0, tangent 0, and cosecant and cotangent undefined because sine has returned to zero. That the numbers repeat is the entire content of periodicity, and it i...

ANGLE

UNIT

COMMON ANGLES

SIN 360°

0.000000

EXACT

360.0000° = 6.283185 rad = 400.0000 grad · on an axis · reference angle 0.00°

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HOW TO USE

1
This page opens with 360° 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 360° 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°

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Last updated: July 28, 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.