What are sin, cos and tan of 120 degrees?

Sine of 120° is √3/2, or 0.866025 as a decimal. Cosine is −1/2, which is -0.500000. Tangent is −√3, or -1.732051. The reference angle is 60°, so all three magnitudes are the 60° magnitudes with signs set by quadrant 2.

What are csc, sec and cot of 120 degrees?

Cosecant is 1 over sine, giving 1.154701. Secant is 1 over cosine, giving -2.000000. Cotangent is 1 over tangent, giving -0.577350. At least one of these lands on an exact whole number, which happens whenever the function it inverts is exactly one half.

What is 120 degrees in radians?

120° is 2π/3 radians, which is 2.094395 as a decimal, and 133.3333 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 120° is 33.3333% of a complete revolution.

Which quadrant is 120 degrees in?

Quadrant 2, with a reference angle of 60°. That means the acute angle between the radius and the horizontal axis is 60°, so every value here has the same magnitude as the corresponding value at 60°, differing only in sign. In quadrant 2 the positive functions are sine and cosecant.

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.

What is the cofunction relationship?

Each function of an angle equals its co-function of the complement: sin θ = cos(90° − θ), tan θ = cot(90° − θ), sec θ = csc(90° − θ). That is where the "co" in cosine, cotangent and cosecant comes from — they are the functions of the complementary angle. It is why 30° and 60° trade values, and it halves how much you actually need to remember.

Can sine or cosine ever exceed 1?

Never, for a real angle. Both are coordinates of a point on a circle of radius 1, so neither can be more than 1 or less than −1. That constraint is a genuinely useful error check: if a calculation hands you a sine of 1.4, you have made a mistake or the problem has no solution. It is exactly how the ambiguous triangle case detects an impossible triangle. Secant and cosecant, being their reciprocals, obey the opposite rule and can never lie strictly between −1 and 1.

Trigonometric Values of 120°

One hundred and twenty degrees is the first angle on this list where a value goes negative, and it is the cleanest place to learn how the sign rules actually work. The point has swung past vertical into the second quadrant, up and to the left, so its horizontal coordinate is negative while its verti...

ANGLE

UNIT

COMMON ANGLES

SIN 120°

0.866025

EXACT

√3/2

120.0000° = 2.094395 rad = 133.3333 grad · quadrant 2 · reference angle 60.00°

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HOW TO USE

1
This page opens with 120° already entered, so every value below is the answer for that angle — sine 0.866025, cosine -0.500000, and the rest — with no typing needed.
2
Read the exact form beside each decimal. At 120° sine is √3/2 and cosine is −1/2, written as surds rather than rounded decimals.
3
Tap any of the six tiles to make it the headline figure. All six functions have finite values at 120°.
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.