Evaluate all six trig functions and their inverses in degrees or radians.
Trigonometric functions relate the angles of a right triangle to the ratios of its sides. Sine is opposite over hypotenuse; cosine is adjacent over hypotenuse; tangent is opposite over adjacent. The reciprocal functions (cosecant, secant, cotangent) are 1/sin, 1/cos, 1/tan. The inverse functions reverse the mapping: given a ratio, they return the angle. Angles are expressed in degrees (0–360) or radians (0–2π).
Right-triangle definitions
sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj
Pythagorean identity
sin²θ + cos²θ = 1
Degree ↔ radian conversion
radians = degrees × π/180
Both measure angles. Degrees divide a full turn into 360 equal parts. Radians measure the arc length on a unit circle: a full turn is 2π radians ≈ 6.2832. Radians are the natural unit in mathematics and physics because formulas like the derivative of sin(x) = cos(x) only hold when x is in radians.
tan(θ) = sin(θ)/cos(θ). At θ = 90°, cos(90°) = 0, so we are dividing by zero. The tangent function has vertical asymptotes at 90°, 270°, and all odd multiples of 90°.
The principal value of arcsin returns angles in [−90°, 90°] (or [−π/2, π/2] in radians). This is the conventional 'main branch'. Other angles with the same sine exist but arcsin always returns the one in this range.