---
epic: 6
story: 6.1
title: "Trigonometric Functions"
status: draft
---

## Epic 6 — Advanced Math & Functions
**Goal:** Scientific, financial, and power-user math.

### Story 6.1: Trigonometric Functions

As a **CalcPad user**,
I want to evaluate trigonometric functions including sin, cos, tan, and their inverses and hyperbolic variants,
So that I can perform scientific and engineering calculations directly in CalcPad.

**Acceptance Criteria:**

**Given** the angle mode is set to radians (default)
**When** the user writes `sin(3.14159)` (approximately pi)
**Then** the result is approximately `0` (within floating-point tolerance)

**Given** the angle mode is set to degrees
**When** the user writes `sin(90)`
**Then** the result is `1`

**Given** the user writes `sin(45°)` with the degree symbol
**When** the engine evaluates the expression
**Then** the engine treats the argument as degrees regardless of the global angle mode setting
**And** the result is approximately `0.7071`

**Given** the engine is in radians mode
**When** the user writes `cos(0)`
**Then** the result is `1`

**Given** the user writes `tan(45°)`
**When** the engine evaluates
**Then** the result is approximately `1`

**Given** the user writes `asin(1)` in radians mode
**When** the engine evaluates
**Then** the result is approximately `1.5708` (pi/2)

**Given** the user writes `acos(0.5)` in degrees mode
**When** the engine evaluates
**Then** the result is `60` (degrees)

**Given** the user writes `atan(1)` in degrees mode
**When** the engine evaluates
**Then** the result is `45`

**Given** the user writes `sinh(1)`
**When** the engine evaluates
**Then** the result is approximately `1.1752`

**Given** the user writes `cosh(0)`
**When** the engine evaluates
**Then** the result is `1`

**Given** the user writes `tanh(0)`
**When** the engine evaluates
**Then** the result is `0`

**Given** the user writes `sin(x)` where `x` is out of domain for an inverse trig function (e.g., `asin(2)`)
**When** the engine evaluates
**Then** an error is displayed indicating the argument is out of the valid domain

**Given** the user wants to switch angle modes
**When** the user sets the mode via a configuration directive (e.g., `angle mode: degrees`)
**Then** all subsequent trig evaluations use the selected mode until changed again