What are the exact values at the special angles?

At 30 degrees sin is 1/2 and cos is sqrt(3)/2; at 45 degrees both sin and cos are sqrt(2)/2; at 60 degrees they swap to sqrt(3)/2 and 1/2. These exact surd forms come from the 30-60-90 and 45-45-90 right triangles.

Why is tan undefined at 90 and 270 degrees?

Tangent equals sin divided by cos, and cos is zero at 90 and 270 degrees. Dividing by zero is undefined, so tan has a vertical asymptote there rather than a finite value.

How do I convert degrees to radians?

Multiply degrees by pi/180. So 180 degrees is pi radians, 90 degrees is pi/2, and 45 degrees is pi/4. The evaluator does this automatically before computing the ratios.

Why do some computed values show tiny non-zero numbers?

Floating-point math introduces minute rounding, so sin(180 degrees) might come out as a value like 1e-16. This tool snaps results extremely close to zero back to 0 so the table stays clean.

Are these values the same on the unit circle?

Yes. On the unit circle a point at angle theta has coordinates (cos theta, sin theta), so the table values are exactly the x and y coordinates at each standard angle, with tan being their ratio y/x.

Trigonometric Values Reference

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Trigonometry rests on a handful of exact values at special angles that show up everywhere from geometry homework to graphics code. This reference lists sin, cos, and tan at the standard angles in both degrees and radians, and adds a live evaluator so you can compute the three ratios for any angle you type.

How it works

The standard table holds exact symbolic values derived from two special right triangles: the 45-45-90 triangle gives sin 45 = cos 45 = √2/2, and the 30-60-90 triangle gives the 1/2 and √3/2 pair at 30 and 60 degrees. On the unit circle, a point at angle θ sits at coordinates (cos θ, sin θ), and tangent is their ratio:

tan(θ) = sin(θ) / cos(θ)

The evaluator first converts your angle to radians using radians = degrees × π/180, then calls the standard sine and cosine routines. Where cosine is effectively zero — at 90 and 270 degrees — tangent is reported as undefined rather than a huge or misleading number, matching its true vertical asymptote.

Tips and example

Memorize the 45-degree row first: sin = cos = √2/2 ≈ 0.7071, tan = 1. The 30 and 60 rows are mirror images of each other.
Past 90 degrees the signs flip by quadrant: in the second quadrant sin stays positive while cos and tan go negative, which the extended table (120, 135, 150 degrees) shows directly.
For radian input, remember π ≈ 3.14159, so entering 1.5708 (≈ π/2) gives sin ≈ 1, cos ≈ 0.

The evaluator is handy for spot-checking a formula or confirming an angle conversion without reaching for a separate calculator.