Trigonometric identities are the most important part of the entire subject - if you read only one page from this course, it should be this one.

We're going to start exploring the following rectangle:

F E C A D B β α 1

Copy the diagram down, and try to fill in all the blanks in the order below.

When you're done, plug in your answers to check them.

  1. Angles

    $\displaystyle{m\angle BDC = }$

    $\displaystyle{m\angle ABF}= $

  2. Sides

    $\displaystyle{AF}= $

    $\displaystyle{AB}= $

    $\displaystyle{BD}= $

    $\displaystyle{FD}= $

    $\displaystyle{BC}= $

    $\displaystyle{CD}= $

    $\displaystyle{DE}= $

    $\displaystyle{FE}= $

  3. Express AB and AF in terms of other sides of the rectangle. Then, substitute the values above to see the trigonometric identities.