Trigonometry Calculator
Enter an angle to get sin, cos and tan at once. Special angles like 30°, 45° and 60° are shown as exact values (1/2, √3/2), with degree and radian support, pi expressions such as pi/6, plus the quadrant signs and the reference-angle working.
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Try an example
Enter an angle to see the values of sin, cos and tan.
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Trigonometry Calculator
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How to use
- 1
Pick the unit
Choose degrees or radians — the same choice as the mode setting on a calculator.
- 2
Enter the angle
Type a number like 30 or a pi expression like pi/6. The example buttons work too.
- 3
Read values and reasons
See sin, cos and tan, the angle in the other unit, the quadrant signs, and the reference-angle working.
Features
- sin, cos and tan shown together, with a clear notice when tan is undefined
- Exact fraction and radical values plus decimals for special angles
- Degree ⇄ radian display on the fly, with pi expressions like pi/6 and 2pi accepted
- Quadrant signs and reference-angle working included; inputs are never transmitted
Use cases
Check trigonometry homework
Verify hand-worked sin, cos and tan values while studying for tests.
Avoid calculator mode errors
See values for degrees and radians side by side to catch unit mix-ups.
Prep for physics vectors
Pull exact sin and cos values before substituting into slopes and wave formulas.
Details
Trigonometric values change completely when the angle unit is wrong. This tool makes you pick the unit (degrees or radians) before entering, which prevents the classic mistake of a calculator sitting in the wrong mode. The angle is also shown converted into the other unit (for example 150° = 5π/6 ≈ 2.618 rad).
For special angles — 30°, 45°, 60° and the axis angles — whose values follow from right triangles and the unit circle, the tool shows exact values such as 1/2, √2/2 and √3 alongside decimal approximations. Other angles are shown as decimals rounded to six places. tan is undefined where cos is 0 (90° and 270°), and the tool reports that instead of a number.
Alongside the values you get the quadrant of the angle with the signs of sin, cos and tan, and for quadrants II–IV the reference angle. For instance sin 150° reads as "quadrant II, reference angle 30°, sin positive", giving sin 30° = 1/2. Inputs are never transmitted; all computation happens locally in your browser.
FAQ
Should I use degrees or radians?
Match the unit of your problem. A symbol like 30° means degrees; an expression like π/6 means radians. The tool shows the value in both units at once, which makes unit mix-ups easy to spot.
How do I remember the special angles?
Derive them from triangles: 30° and 60° come from the 1 : 2 : √3 right triangle, 45° from the 1 : 1 : √2 one. Reading opposite/hypotenuse ratios from a sketch is more reliable than memorizing decimals — the exact-value display here is handy for checking.
Why does tan show "undefined"?
tan = sin/cos, and cos is 0 at 90° and 270°, so the division cannot be done. On the graph these are where tan approaches its asymptotes, so no value exists.
How do I enter angles with pi?
Type pi, pi/6, 2pi or 1.5pi (the π symbol also works). For example, 30° is pi/6 and 45° is pi/4.
Related guide
GuideHow to Calculate Logarithms: Rules, Change of Base and Examples
Calculate logarithms from the definition, including bases below one. Worked change-of-base examples, log vs ln, domain checks, digit-count boundaries, rounded outputs, a diagram and FAQs.
GuideHow to Remember Trig Values: Deriving 30, 45 and 60 Degrees
Learn sin, cos and tan with two triangles and a unit circle. Exact-value tables, 150° and negative-angle signs, degree/radian inputs, undefined tan90° and practical checks.
GuideHow to Find the Dot Product of Two Vectors: Components and Angle
Learn the two formulas for the dot product — a·b = a₁b₁ + a₂b₂ and a·b = |a||b|cosθ — when to use each, how to find the angle between vectors, and what the sign tells you. Worked examples in 2D and 3D, plus a free browser tool.
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Did you know?
sin 90° = 1 simply says that a point standing on the unit circle at 90° is exactly one unit high. Reading sin, cos and tan as height, width and slope on the unit circle bundles in the quadrant signs.