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Lesson 9.9 - Introduction to Trigonometry

Today, we started to look at the ratios that exist in all right triangles - the study of these and how to use them is called Trigonometry. We started by looking at a right triangle which has one 30 degree angle.

With that triangle (shown below), notice that we calculated three ratios - the first being the ratio of the side opposite the angle to the hypotenuse. Also note that these ratios are the same for any right triangle with a 30 degree angle!

Next, we discussed that these ratios are called the sine, cosine, and tangent of the given angle. Since these are commonly used functions, most calculators have them available as buttons. Sketchpad is no different - below, I show that these are the same as the ratios we calculated:

Next, we saw that these ratios change based on the measure of the angle. The table below shows some values for these ratios with different angle measurements:

At this point, I pointed out a great way of remembering these ratios. It's called SOHCAHTOA. Sine = Opposite/Hypotenuse, Cose = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent. Remember that!! We then went through the following example:

To wrap up, we went through the following example: