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Trigonometric Ratios

Kristie Ferrentino MAT 320 Professor Healy Ninth Grade (Algebra). Trigonometric Ratios. Objective. To discover the three main trigonometric ratios. To use trigonometric ratios in finding an angle for a right triangle. Trigonometry.

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Trigonometric Ratios

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  1. Kristie Ferrentino MAT 320 Professor Healy Ninth Grade (Algebra) Trigonometric Ratios

  2. Objective • To discover the three main trigonometric ratios. • To use trigonometric ratios in finding an angle for a right triangle.

  3. Trigonometry • Trigonometry: is the study of the relationships among the angles and sides of triangles. • Trigonometric Ratio: is a ratio that compares the side lengths of two sides of a right triangle • Three most common trigonometric ratios are sine, cosine, and tangent.

  4. Naming Sides of Right Triangles • a (adjacent): is the length of the side adjacent to the angle () • o (opposite): is the length of the side opposite the angle • h (hypotenuse): is the length of the side across from the right angle Hypotenuse o h Opposite a Adjacent Hypotenuse Adjacent h a o Opposite

  5. Trigonometric Ratios • The three trigonometric ratios are just the length of one side divided by another. • For a right triangle with an angle  Hypotenuse o h Opposite a Adjacent

  6. SOH CAH TOA • A way to remembering how to compute the sine, cosine, and tangent of an angle • SOH stands for • CAH stands for • TOA stands for Opp Hyp  Adj

  7. How to Use Trig Ratios Find the sine, cosine, and tangent of angle K. Example: Find the measure of angle K, to the nearest degree. J 15 9 h o a  L K 12 Use a scientific calculator to find the angle measure with a sine of 9/15. Enter: 2nd[cos-1(9/15)] Result: 36.8699 So. m<K  37

  8. Find the Trig Ratios Find the values of the three trigonometric ratios for angle C. A 1. 2. A 15 3. A C 5 9 3 15 8 B 17 B 4 C 12 C B

  9. Solving for Unknown Angle Find the measurement of angle L for each right triangle to the nearest degree, by using one of the trig ratios. L 1. 2. N 15 3. K J 5 5 8 M P 4 A 12 L L L  53.1301 L 53 L  22.6199 L  23 L  57.769 L  58

  10. Value of the Trig Ratios Find the value of the trigonometric ratio to the nearest ten-thousandth. (Use a scientific calculator to help you.) • Cos 68 • Tan 14 • Sin 37 • Cos 82 • Sin 85  .374607 .3746  .249328  .2493  .601815  .6018  .139173  .1391  .996195  .9962

  11. What did we learn today? • What is a trigonometry? • What are the trigonometric ratios? • What are the sides of a right triangle called? • How can we remember the trig ratios?

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