Sin Cos Tan Calculator

A sin/cos/tan calculator evaluates the three primary trigonometric functions — sine, cosine, and tangent — for any angle, plus their reciprocals (cosecant, secant, cotangent). You feed in an angle in degrees or radians and get back the six function values, accurate to six decimal places. It's the digital replacement for the trig tables that used to fill the back of every textbook.

Trigonometry connects angles to ratios of sides in right triangles, and more generally to coordinates on the unit circle. That makes these functions essential for everything from surveying a roof pitch and calculating a projectile's trajectory to running the matrix math behind 3D graphics. The calculator handles the conversion between degree and radian inputs internally so you don't have to.

Compute the trig functions for θ = 45°:

• sin(45°) = √2 / 2 ≈ 0.707107
• cos(45°) = √2 / 2 ≈ 0.707107
• tan(45°) = sin/cos = 1 exactly
• csc(45°) = 1/sin ≈ 1.414214 (= √2)
• sec(45°) = 1/cos ≈ 1.414214
• cot(45°) = 1/tan = 1

A 45° angle in a right triangle implies an isosceles right triangle, so the two legs are equal — that's why sin and cos are identical and tan comes out to exactly 1. Try 30° and 60° next; you'll see the classic 1/2, √3/2 pattern.

• Construction and carpentry — finding rafter lengths from roof pitch, ramp slopes, or stair stringers.
• Physics homework — resolving force or velocity vectors into x and y components (Fx = F·cos θ, Fy = F·sin θ).
• Navigation and surveying — converting bearings and distances to coordinates.
• Game and graphics programming — rotating sprites, generating circular motion, or computing camera angles.
• Electronics — phase relationships in AC signals where voltage = V₀·sin(ωt + φ).

• Wrong unit setting. sin(90) returns 0.894 in radian mode but 1.000 in degree mode. Always confirm which unit you mean before reading the result.
• Confusing sin⁻¹ with 1/sin. sin⁻¹(x) means arcsine (the inverse function), not the reciprocal. The reciprocal of sin is cosecant.
• Forgetting tan is undefined at 90°, 270°, etc. Cosine hits zero there, so tan blows up. The calculator returns "undefined" for these inputs.
• Mixing up opposite and adjacent. Opposite is across from the angle of interest; adjacent is next to it (and isn't the hypotenuse).
• Rounding too early. If you round sin(30°) to 0.5 and then square it for an identity check, you lose precision. Carry full digits until the final step.