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Trigonometric Ratios: How to Use Trig Ratios

Learn about trigonometric ratios in a right triangle, including sine, cosine, and tangent. Discover how to label sides, find ratios, and use SOHCAHTOA method. Practice with examples and homework assignments.

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Trigonometric Ratios: How to Use Trig Ratios

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  1. Trigonometric Ratios How do we use trig ratios? M2 Unit 2: Day 3

  2. So, if one angle is Then the other one is In a Triangle, we know that the angles have a sum of 180 and that the two acute angles are complementary

  3. Assume X Z Y

  4. Trigonometric Ratios: Are ratios of the lengths of 2 sides of a right triangle. • There are 3 basic trig ratios: sine, cosine, and tangent (abbreviated sin, cos, and tan) • The value of a trig ratio depends only on the measure of the acute angle, not on the particular triangle being used to compute the value.

  5. SOHCAHTOA • If you can remember his name, then you can remember your trig ratios!

  6. Opposite means “across from the angle” • Adjacent means “attached to the angle” • Hypotenuse is always opposite the right angle.

  7. Label the hypotenuse, opposite and adjacent for angle A. B C A

  8. Label the hypotenuse, opposite and adjacent for angle .

  9. Label the hypotenuse, opposite and adjacent for angle X. X Z Y Now, label the hypotenuse, opposite and adjacent for angle y.

  10. Now find the sine, the cosine, and the tangent of . • Notice something about the sine and cosine ratios? • How about the tangent ratios?

  11. 2 13 5 12 Now find the sine, the cosine, and the tangent of . • Notice something about the sine and cosine ratios? • How about the tangent ratios?

  12. Tan = ≈0.9524 Find tan . Round to four decimal places. C 42 40 B A 58

  13. Find sin and tan . Write each answer as a decimal rounded to four decimal places. 45 B C 28 53 A

  14. Example 3: Use your calculator to approximate the given value to four decimal places. You can use your calculator to find a decimal approximation for trig ratios. a) sin 82° b) cos 30° c) tan 60° Solutions: 0.9903 0.8660 1.7321

  15. In summary, notice 4 things: • The 2 acute angles of a right triangle are always complementary • The sin, cos, and tan of congruent angles in similar triangles are always equal no matter the side lengths • The sin and cos ratios of 2 complementary angles are always switched • The tan ratios of 2 complementary angles are always reciprocals of one another

  16. Homework: • Page 159 (#1, 3, 7) and • Page 166 (#2-14 even)

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