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7.2 Right Triangle Trigonometry

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. Hypotenuse. Side opposite . . Side adjacent to .

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7.2 Right Triangle Trigonometry

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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

  2. Hypotenuse Side opposite  Side adjacent to  The sides of a right triangle 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 .

  3. Trigonometric Functions • 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: • Sine • Cosine • Tangent • Cosecant • Secant • Cotangent

  4. Six Trigonometric Functions

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

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

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

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

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

  10. This is known as a Pythagorean Identity.

  11. Divide each side by cos2 x to derive 2nd Pythagorean Identity.

  12. Divide each side by sin2 x to derive 3rd Pythagorean Identity.

  13. End of Section 7.2

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