What are sin, cos and tan of 30 degrees?

Sine of 30° 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 1.

What are csc, sec and cot of 30 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 30 degrees in radians?

30° is π/6 radians, which is 0.523599 as a decimal, and 33.3333 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 30° is 8.3333% of a complete revolution.

Which quadrant is 30 degrees in?

Quadrant 1, 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 1 the positive functions are all six.

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.

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.

Trigonometric Values of 30°

Thirty degrees gives trigonometry its cleanest number. Sine of 30° is exactly one half — not 0.49999999999999994, which is what a computer working in radians will quietly hand you, but exactly 1/2 — and the reason is a piece of geometry you can draw in ten seconds. Take an equilateral triangle with ...

ANGLE

UNIT

COMMON ANGLES

SIN 30°

0.500000

EXACT

1/2

30.0000° = 0.523599 rad = 33.3333 grad · quadrant 1 · reference angle 30.00°

Created with❤️byeaglecalculator.com

HOW TO USE

1
This page opens with 30° 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 30° 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 30°.
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.