What are sin, cos and tan of 60 degrees?

Sine of 60° 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 1.

What are csc, sec and cot of 60 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 60 degrees in radians?

60° is π/3 radians, which is 1.047198 as a decimal, and 66.6667 gradians. The conversion is degrees times π divided by 180, since a full turn of 360° is 2π radians. Put another way, 60° is 16.6667% of a complete revolution.

Which quadrant is 60 degrees in?

Quadrant 1, 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 1 the positive functions are all six.

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.

How does this connect to waves?

Directly. Plot the vertical coordinate of a point moving steadily round the unit circle against time and you have drawn a sine wave — the circle is the definition and the wave is its shadow. That is why the same functions describe alternating current, sound, light, tides and any oscillation at all. The angle becomes a phase, a full turn becomes one cycle, and the periodicity you see in these values becomes the frequency.

What is the fastest way to memorise all of this?

Learn the first quadrant and one triangle. The 30-60-90 triangle with sides 1, √3 and 2 gives every value at 30° and 60°; the 45-45-90 triangle with sides 1, 1 and √2 gives 45°. Then learn the axis values at 0° and 90° from the unit circle, which needs no triangle at all. Everything else is a reference angle and a sign, and no further memorisation is required or useful.

Why is one value exact and another a long decimal?

Because some trigonometric values are rational or simple surds and others are not. Sine of 30° is exactly one half, a number that can be written down completely. Sine of 40° is an irrational number with no closed form in surds, so any decimal is a truncation. Every value at a multiple of 30° or 45° falls in the first category, which is precisely why those angles are the ones worth memorising — you can write them exactly rather than approximately.

Trigonometric Values of 60°

Sixty degrees is the other half of the same triangle that gives you 30°, and the relationship between the two is the most useful symmetry a beginner can learn. Cut an equilateral triangle of side 2 down the middle and you get a right triangle with angles of 30°, 60° and 90°, sides of 1, √3 and 2. Lo...

ANGLE

UNIT

COMMON ANGLES

SIN 60°

0.866025

EXACT

√3/2

60.0000° = 1.047198 rad = 66.6667 grad · quadrant 1 · reference angle 60.00°

Created with❤️byeaglecalculator.com

HOW TO USE

1
This page opens with 60° 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 60° 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 60°.
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.