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Section 5.2 Right Triangle Trigonometry

What you should learn How to evaluate trigonometric functions of acute angles. Section 5.2 Right Triangle Trigonometry. Objective: In this lesson you learned how to evaluate trigonometric functions of acute angles and how to use the fundamental trigonometric identities.

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Section 5.2 Right Triangle Trigonometry

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  1. What you should learn How to evaluate trigonometric functions of acute angles Section 5.2 Right Triangle Trigonometry Objective: In this lesson you learned how to evaluate trigonometric functions of acute angles and how to use the fundamental trigonometric identities.

  2. I. The Six Trigonometric Functions In the right triangle shown below, label the three sides of the triangle relative to the angle labeled θ as (a) the hypotenuse, (b) the opposite side, and (c) the adjacent side.

  3. Abbreviations of the six functions. • Using the lengths of these three sides, six ratios can be formed that define the following six trigonometric functions of the acute angle θ. • List the abbreviation for each trigonometric function.

  4. Definitions of the six functions. • Let θ be an acute angle of a right triangle. Define the sixtrigonometric functions of the angle θ using opp = the length of the side opposite θ, adj = the length of the side adjacent to θ, and hyp = the length of the hypotenuse.

  5. Definitions of the six functions. The cosecant function is the reciprocal of the _________ function. The cotangent function is the reciprocal of the __________ function. The secant function is the reciprocal of the ___________ function.

  6. The Six Trigonometric Functions Side opposite θ Hypotenuse θ Side adjacent θ

  7. Example 1: • In the right triangle below, find sin θ, cos θ, and tan θ.

  8. Give the sines, cosines, and tangents of the following special angles:

  9. Cofunctions Cofunctions of complementary angles are ____________ . If θ is an acute angle, then: equal

  10. II. Trigonometric IdentitiesReciprocal Identities What you should learn How to use the fundamental trigonometric identities

  11. List two quotient identities:

  12. List three Pythagorean identities:

  13. III. Evaluating Trigonometric Functions with a Calculator • To evaluate the secant function with a calculator, . . . What you should learn How to use a calculator to evaluate trigonometric functions

  14. Example 2: Use a calculator to evaluate (a) tan 35.4° (b) cos 3 Remember to change modes (a) = .7106630094 (b) = -.9899924966

  15. IV. Applications Involving Right Triangles • What does it mean to “solve a right triangle?” • An angle of elevation is . . . • An angle of depression is . . .

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