1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles Use Fundamental Identities Use the Complimentary Angle Theorem

2 Take a look at the right triangle, with an acute angle, , in the figure below. Notice how the three sides are labeled in reference to . The sides of a right triangle  Side adjacent to  Side opposite  Hypotenuse We will be reviewing special ratios of these sides of the right triangle, with respect to angle, . These ratios are better known as our six basic trig functions.

3 Six Trigonometric Functions

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5 To remember the definitions of Sine, Cosine and Tangent, we use the acronym : “SOH CAH TOA” Definitions of the Six Trigonometric Functions

6 Find the exact value of the six trig functions of  : Example  5 9

7 Given that  is an acute angle and, find the exact value of the six trig functions of . Example

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9 find the four remaining trig functions of angle  in simplest form.

This is known as a Pythagorean Identity. 10 For the right triangle shown, the Pythagorean Theorem gives us:

11 Divide each side by cos 2  to derive 2 nd Pythagorean Identity.

12 Divide each side by sin 2  to derive 3 rd Pythagorean Identity.

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14 Find the exact value of each expression using the Fundamental Identities. Do NOT use a calculator.

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18 Find the exact value of each expression using the Complementary Angle Theorem. Do NOT use a calculator.

19 End of Section 7.2