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An Easy Way to Visualize Certain Common Trig Values

 

Here's a method for visually remembering various Sin, Cos, and Tan values for angles that you'll encounter frequently when using trig.

 

First visualize the following two diagrams:

      The first is a square with a side of length 1--

Unit Square

        Note the diagonal (the red dashed line) drawn. We use the Pythagorean Theorem to determine its length.

      The second is an equilateral triangle with sides of length 2 --

Unit Triangle

        Note the line (the red dashed line) drawn from the top of the triangle to a point perpendicular to the base of the triangle. Once again we use the Pythagorean Theorem to determine the length of the added line.

Next, referring to these two diagrams and remembering SOH, CAH, TOA, we can create the following table:

Trig Function Values Table

 

Now you no longer have to look up these values in a trig table. You can visualize them and have those values at your fingertips.

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Last Updated:

Sunday, January 20, 2008