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Understanding Trigonometric Functions: Ratios & Applications Q&A

Learn the six trigonometric functions and their applications in solving real-world right triangle problems. Understand trigonometric ratios of sides in right triangles and reciprocal functions. Practice finding exact and approximate values using trigonometry. Checkpoints and assignments included for reinforcement.

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Understanding Trigonometric Functions: Ratios & Applications Q&A

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  1. Warm-Up 8/13 What are the six trigonometric functions and the ratios? Q&A on yesterday’s assignment.

  2. Rigor:You will learn the six trigonometric functions and how to use them to solve problems.Relevance:You will be able to solve real world right triangle trigonometry problems using the six trigonometric functions.

  3. 4-1a Right Triangle Trigonometry

  4. Trigonometric Ratios: ratios of sides of a right triangle. hypotenuse hyp opposite adj adjacent opp

  5. 6 Trigonometric Ratios: 3 basic: 3 additional:

  6. Reciprocal Functions

  7. Example 1: Find the exact values of the 6 Trigonometric functions of 7 hyp θ adj 3 opp

  8. Since any two right triangles with angle are similar, these ratios are the same, regardless of the size of the triangle. 50 30 5 3 4 40

  9. Example 2: If , find the exact values of the 5 remaining trigonometric functions. 3 1

  10. not ° 7 hyp x Example 3: Find the value of . Round to the nearest tenth, if necessary. adj Make sure your calculator is in degrees.

  11. not hyp 12 Example 5: Use a trigonometric function to find the measure of . Round to the nearest degree. 15.7 opp

  12. 4-1a Checkpoints: TX p222, 3A; p223, 5A math! Find the measure of . Find the value of . • 4-1a Assignment: TX p227, 3-36 DB3

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