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Trigonometry

Trig equations, identities, inverse functions, and complex numbers — exact symbolic answers with every step shown.

What Zeretis can solve

Zeretis solves trigonometric problems exactly — returning exact values like π/6, √3/2, and 2π/3 rather than decimal approximations. It handles both algebraic manipulation of trig expressions and equation solving.

Trig equations

Solve for all solutions in [0, 2π] or the general solution. Handles compound angles.

Identity verification

Prove or simplify trig expressions using standard identities.

Inverse functions

arcsin, arccos, arctan — exact values for standard angles, expressions for others.

Unit circle values

Exact values for sin, cos, tan at any standard angle.

Polar coordinates

Convert between Cartesian and polar, work with polar equations.

Complex numbers

Polar form, De Moivre's theorem, complex roots of unity.

How to type trigonometry problems

Trig equation

solve sin(x) = sqrt(3)/2 for x in [0, 2pi]

→ x = π/3, x = 2π/3

Simplification

simplify sin^2(x) + cos^2(x)

→ 1

Exact value

cos(5pi/6)

→ −√3/2

Complex number

convert 1 + i to polar form

→ √2 · e^(iπ/4)

Identity

expand cos(2x) using double angle formula

→ cos²(x) − sin²(x) = 2cos²(x) − 1 = 1 − 2sin²(x)

Best practices

Use pi for π — the solver understands pi, π, and 3.14159 but exact form is better
Specify the solution domain when needed: "in [0, 2π]" or "general solution"
For inverse trig: arcsin, arccos, arctan or asin, acos, atan all work
The solver returns exact values — sin(30°) gives 1/2, not 0.5
Degrees and radians: specify "degrees" if needed, otherwise radians are assumed
For complex numbers: use i for the imaginary unit

📐Algebra ∫Calculus 🔀Differential Equations 🔢Linear Algebra ∑Series & Sequences

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