Parametric Functions and Vectors: Background You’ll Need 2

  • Use inverse tangent to find an unknown angle

When you know the sides of a right triangle, you can find the angle using the inverse tangent function, written as [latex]\tan^{-1}[/latex] or arctan.

In a right triangle, the opposite side is 4 units long and the adjacent side is 3 units long.
Find the measure of the angle [latex]\theta[/latex].

Use the definition of tangent:
[latex]\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}}[/latex]

Substitute:
[latex]\tan(\theta) = \dfrac{4}{3}[/latex]

Take the inverse tangent:
[latex]\theta = \tan^{-1}\left(\dfrac{4}{3}\right)[/latex]

Use a calculator in degree mode:
[latex]\begin{align} \theta &\approx \tan^{-1}(1.3333) \\ \theta &\approx 53.13^\circ \end{align}[/latex]

Make sure your calculator is in the correct mode (degrees or radians).

On a TI-84 Calculator:

  1. Press MODE → set to DEGREE.

  2. Type 2ND → TAN → (height ÷ width) → ENTER.