Sin Cos Tan Calculator

How to Use This Calculator

1. Enter an angle and select degrees or radians.
2. All six trig values (sin, cos, tan, csc, sec, cot) are computed instantly.
3. Use From Sides tab to compute trig ratios from triangle side lengths.
4. Use Inverse tab to find the angle from a known trig value.

Formula

Example

Frequently Asked Questions

• What are sin, cos, and tan? ▼
  In a right triangle, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent, where θ is one of the acute angles. These ratios extend to all angles using the unit circle: for angle θ, the point on the unit circle is (cos θ, sin θ). Sine and cosine range from −1 to 1; tangent ranges from −∞ to +∞. The mnemonic SOH-CAH-TOA (Sine=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, Tangent=Opposite/Adjacent) helps remember these definitions.
• What is csc, sec, and cot? ▼
  Cosecant, secant, and cotangent are the reciprocal functions of the three primary trig functions: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), and cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). They are undefined wherever the denominator is zero: csc is undefined where sin = 0 (at 0°, 180°, 360°, …), sec where cos = 0 (at 90°, 270°, …), and cot where sin = 0. These functions appear in calculus integrals (e.g., ∫sec²(x)dx = tan(x)+C) and in physics problems involving angles.
• How do I convert degrees to radians? ▼
  Multiply degrees by π/180 to get radians. Examples: 45° = π/4 ≈ 0.7854 rad, 90° = π/2 ≈ 1.5708 rad, 180° = π rad, 360° = 2π rad. To convert radians back to degrees, multiply by 180/π. Key values: π/6 = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°. Most science and engineering calculations use radians. This calculator accepts both — just select Degrees or Radians mode before entering your angle.
• What is sin(30°)? ▼
  sin(30°) = 1/2 = 0.5 exactly. This comes from the 30-60-90 right triangle: with hypotenuse 2, the side opposite 30° = 1 and the side opposite 60° = √3. So sin(30°) = 1/2, cos(30°) = √3/2 ≈ 0.866, tan(30°) = 1/√3 ≈ 0.577. For the 45-45-90 triangle: sin(45°) = cos(45°) = √2/2 ≈ 0.707. For 60°: sin(60°) = √3/2 ≈ 0.866. These special angles are the most commonly memorized in trigonometry.
• Why is tan(90°) undefined? ▼
  tan(θ) = sin(θ)/cos(θ). At θ = 90°, sin(90°) = 1 but cos(90°) = 0, making the expression 1/0 — which is undefined. On the unit circle, 90° points straight up. The geometric tangent line at this point is vertical and never intersects the x-axis, so there is no finite tangent value. As θ approaches 90° from below, tan(θ) → +∞; from above, tan(θ) → −∞. tan is also undefined at 270° and all angles of the form 90° + 180°n (every odd multiple of 90°).

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