Introduction to Right Triangle Trigonometry

Learning Objectives

By the end of this section, you will be able to:

  • Use right triangles to evaluate trigonometric functions.
  • Find function values for [latex]30^\circ \left(\frac{\pi }{6}\right)[/latex], [latex]45^\circ \left(\frac{\pi }{4}\right)[/latex], and [latex]60^\circ \left(\frac{\pi }{3}\right)[/latex].
  • Use cofunctions of complementary angles.
  • Use the deļ¬nitions of trigonometric functions of any angle.
  • Use right triangle trigonometry to solve applied problems.

We have previously defined the sine and cosine of an angle in terms of the coordinates of a point on the unit circle intersected by the terminal side of the angle:

[latex]\begin{array}{c}\cos \text{ }t=x\\ \sin \text{ }t=y\end{array}[/latex]
In this section, we will see another way to define trigonometric functions using properties of right triangles.