Inverse Trig Calculator

Inverse Trig is evaluated from Function and Input Value. The calculation reports Angle, Angle and Angle.

Results

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About the Inverse Trig Calculator

Inverse Trig is treated here as a quantitative relation between Function and Input Value and Angle, Angle and Angle.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
arcsin(x) = angle whose sine is x
arccos(x) = angle whose cosine is x
arctan(x) = angle whose tangent is x

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

arcsin(x) = angle whose sine is x
arccos(x) = angle whose cosine is x
arctan(x) = angle whose tangent is x

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Roof Pitch Angle

Inputs

function: arctan (tan⁻¹) value: 0.5
Angle: 30 deg. Angle: 0.52359878 rad. Angle: 33.333333 grad

With Input Value = 0.5 as the stated inputs, the result is Angle = 30 deg, Angle = 0.52359878 rad and Angle = 33.333333 grad. Each value corresponds to the declared output fields.

Example 2: Projectile Launch Angle

Inputs

function: arcsin (sin⁻¹) value: 0.866
Angle: 59.997089 deg. Angle: 1.04714675 rad. Angle: 66.663432 grad

With Input Value = 0.866 as the stated inputs, the result is Angle = 59.997089 deg, Angle = 1.04714675 rad and Angle = 66.663432 grad. Each value corresponds to the declared output fields.

Example 3: Ramp Angle — ADA Compliance Check

Inputs

function: arctan (tan⁻¹) value: 0.0833
Angle: 4.778275 deg. Angle: 0.08339664 rad. Angle: 5.309195 grad

With Input Value = 0.0833 as the stated inputs, the result is Angle = 4.778275 deg, Angle = 0.08339664 rad and Angle = 5.309195 grad. Each value corresponds to the declared output fields.

Example 4: Viewing Angle — Stadium Design

Inputs

function: arccos (cos⁻¹) value: 0.342
Angle: 19.998772 deg. Angle: 0.34904441 rad. Angle: 22.220858 grad

With Input Value = 0.342 as the stated inputs, the result is Angle = 19.998772 deg, Angle = 0.34904441 rad and Angle = 22.220858 grad. Each value corresponds to the declared output fields.

Common Use Cases

  • Find angle from a known trig ratio
  • Calculate launch angle in physics
  • Determine roof pitch angle from rise/run
  • Find viewing angle in architecture