Use One Function to Solve for Another Function

By Mary Jane Sterling

Sometimes you have to solve for a trig function in terms of another function. In the following example, the cosine of angle lambda is 12/13. What are the values of the sine and tangent of lambda?

  1. Identify the sides given by the cosine function.

    The cosine ratio is adjacent/hypotenuse. Using the given ratio, the adjacent side measures 12 units, and the hypotenuse measures 13 units.

  2. Find the measures of the missing side.

    Using the Pythagorean theorem, you find that the missing side (the opposite side) measures 5 units.


  3. Determine the values of the sine and tangent.

    The sine is opposite/hypotenuse and the tangent is opposite/adjacent, so