All six trig functions of any angle — sin, cos, tan, cot, sec, csc — in degrees or radians, with the angle reduced, its quadrant signs, and a classic values table.
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What the six functions measure
Picture the angle drawn on a unit circle: sin is the y-coordinate of the point on the rim, cos is the x-coordinate, and tan = sin ÷ cos is the slope of the radius. The other three are reciprocals — csc = 1/sin, sec = 1/cos, cot = 1/tan — and share the sign of their partner.
Degrees vs radians
A full circle is 360° or 2π radians, so radians = degrees × π/180 (30° = π/6 ≈ 0.5236 rad). Radians are the natural unit — in radians, sin x ≈ x for small angles — but the unit must be stated. Interpreting 30 as radians gives sin 30 rad ≈ −0.988, a completely different answer from 0.5.
Quadrants and signs
The mnemonic All–Sin–Tan–Cos tracks the signs: in Quadrant I everything is positive; in II only sin (and csc); in III only tan (and cot); in IV only cos (and sec). The result board names your quadrant and summarizes the signs after reducing the angle into [0°, 360°).
Rows: sin 35° = 0.573576, cos 35° = 0.819152, tan 35° = 0.700208.
Over a 12-foot run the rise is 12 × tan 35° = 8.40 feet.
How to use it
Pick degrees or radians to match your problem — the mode is where most mistakes live.
Type any angle; it is reduced to 0–360° before the functions are taken.
Read all six function values plus the quadrant and sign summary.
Sanity-check against the classic-angles table under the result.
Frequently asked questions
How do I evaluate the six trig functions in degrees?
Convert to radians by multiplying by π/180, then take the functions of that angle: sin 30° = sin(π/6) = 0.5. The calculator shows the reduced angle in degrees, radians, and π-multiples so you can verify each step.
Why is tan 90° undefined?
tan = sin ÷ cos, and cos 90° = 0. Division by zero has no finite value, so the tangent curve runs off toward infinity at that point — already at 89.9° the tangent is about 573.
Which functions are positive in each quadrant?
All–Sin–Tan–Cos: everything is positive in Quadrant I, sine (with csc) in II, tangent (with cot) in III, and cosine (with sec) in IV. A reciprocal always shares the sign of the function it inverts.
What is the difference between degree mode and radian mode?
The same number names a different angle: 30 radians is about 1,719°. Always check the mode before trusting a result — the wrong mode changes both magnitude and sign silently.
What are cot, sec, and csc?
The reciprocals of the big three: cot = cos/sin, sec = 1/cos, csc = 1/sin. Where the partner function equals zero, the reciprocal is undefined rather than zero — inverting a zero is not possible.