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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

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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.

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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

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Find the value of each of the six trigonometric functions of the angle .

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7 Find the exact value of the six trig functions of : Example 5 9 Hint: First find the length of the hypotenuse using the Pythagorean Theorem.

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8 Example (cont) 5 9 So the six trig functions are:

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

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This is known as a Pythagorean Identity.

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

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

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21 End of Section 7.2

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