What are sin, cos and tan of 270 degrees?

Sine of 270° is −1, or -1.000000 as a decimal. Cosine is 0, which is 0.000000. Tangent is undefined, because cosine is exactly zero here and tangent divides by it. 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 tan and sec undefined at 270 degrees?

Because they are divisions and the denominator is exactly zero. Tangent is sine over cosine and secant is 1 over cosine, and cosine of 270° is exactly 0, so both divide by zero. Neither has a value — not a very large one, but none at all. The remaining functions are perfectly well behaved: sin 270° = -1.000000, cos 270° = 0.000000, csc 270° = -1.000000, cot 270° = 0.000000.

What is 270 degrees in radians?

270° is 3π/2 radians, which is 4.712389 as a decimal, and 300.0000 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 270° is 75.0000% of a complete revolution.

Why does 270 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 270° 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 90°.

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.

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.

Trigonometric Values of 270°

Two hundred and seventy degrees is three quarters of a turn, and it is the second and last place on a single revolution where trigonometry breaks. The point has swung all the way to the bottom of the unit circle, at coordinates (0, −1), so sine is exactly −1, its most negative possible value, and co...

ANGLE

UNIT

COMMON ANGLES

SIN 270°

-1.000000

EXACT

−1

270.0000° = 4.712389 rad = 300.0000 grad · on an axis · reference angle 90.00°

Created with❤️byeaglecalculator.com

HOW TO USE

1
This page opens with 270° already entered, so every value below is the answer for that angle — sine -1.000000, cosine 0.000000, and the rest — with no typing needed.
2
Read the exact form beside each decimal. At 270° 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 tan and sec 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 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.