Question

First use the Pythagorean theorem to find the exact length of the missing side. Then find the exact values of the six trigonometric functions for angle 0.

Answer 1

The trigonometric functions are given by the following formulas:

`\begin{gathered} \sin \theta=(a)/(h) \\ \cos \theta=(b)/(h) \\ \tan \theta=(a)/(b) \\ \cot \theta=(b)/(a) \\ \sec \theta=(h)/(b) \\ \csc \theta=(h)/(a) \end{gathered}`

Where we call a to the opposite leg to the angle θ (the side whose measure equals 20), b is the adjacent leg to angle θ (the side whose measure equals 21) and we call h to the hypotenuse (the larger side, whose measure equals 29).

By replacing 20 for a, 21 for b and 29 for h into the above formulas, we get:

`\begin{gathered} \sin \theta=(20)/(29) \\ \cos \theta=(21)/(29) \\ \tan \theta=(20)/(21) \\ \csc \theta=(29)/(20) \\ \sec \theta=(29)/(21) \\ \cot \theta=(21)/(20) \end{gathered}`