What are sin, cos and tan of 210 degrees?

Sine of 210° is −1/2, or -0.500000 as a decimal. Cosine is −√3/2, which is -0.866025. Tangent is √3/3, or 0.577350. The reference angle is 30°, so all three magnitudes are the 30° magnitudes with signs set by quadrant 3.

What are csc, sec and cot of 210 degrees?

Cosecant is 1 over sine, giving -2.000000. Secant is 1 over cosine, giving -1.154701. Cotangent is 1 over tangent, giving 1.732051. At least one of these lands on an exact whole number, which happens whenever the function it inverts is exactly one half.

What is 210 degrees in radians?

210° is 7π/6 radians, which is 3.665191 as a decimal, and 233.3333 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 210° is 58.3333% of a complete revolution.

Which quadrant is 210 degrees in?

Quadrant 3, with a reference angle of 30°. That means the acute angle between the radius and the horizontal axis is 30°, so every value here has the same magnitude as the corresponding value at 30°, differing only in sign. In quadrant 3 the positive functions are tangent and cotangent.

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.

Why does a calculator sometimes disagree with the exact value?

Because it is working in radians and converting. An angle like 30° becomes π/6, which is irrational and cannot be stored exactly in binary, so the stored value is a hair off and the sine comes back as 0.49999999999999994 rather than 0.5. The error is around one part in ten thousand million million and matters for nothing practical, but it does mean a comparison against 0.5 fails. This page looks up the special angles rather than computing them, so the exact values really are exact.

Trigonometric Values of 210°

Two hundred and ten degrees drops into the third quadrant, and it is the first angle on this list where both coordinates are negative at once. The point sits down and to the left, so sine and cosine are both negative — sine is −1/2 and cosine is −√3/2, the same magnitudes you get at 30° because the ...

ANGLE

UNIT

COMMON ANGLES

SIN 210°

-0.500000

EXACT

−1/2

210.0000° = 3.665191 rad = 233.3333 grad · quadrant 3 · reference angle 30.00°

Created with❤️byeaglecalculator.com

HOW TO USE

1
This page opens with 210° already entered, so every value below is the answer for that angle — sine -0.500000, cosine -0.866025, and the rest — with no typing needed.
2
Read the exact form beside each decimal. At 210° sine is −1/2 and cosine is −√3/2, 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 210°.
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.