Bell Work: Perform the calculation and express the answer with the correct number of significant digits. 1.24g + 6.4g + 5.1g

Answer: 12.7g

Lesson 118: Sine, Cosine, Tangent

In lesson 112, we practiced finding the ratios of lengths of sides of right triangles. These ratios have special names.

Trigonometry Ratios: Name Ratio Sine Opposite/Hypotenuse Cosine Adjacent/Hypotenuse Tangent Opposite/Adjacent SOH CAH TOA

Example: Find the sine, cosine and tangent of <A. B 10 6 A C 8

Answer: Sine <A = 6/10 = 0. 6 Cosine <A = 8/10 = 0 Answer: Sine <A = 6/10 = 0.6 Cosine <A = 8/10 = 0.8 Tangent <A = 6/8 = 0.75

Notice that we express each ratio as a decimal Notice that we express each ratio as a decimal. The “trig” ratios for this angle happen to be rational numbers. Since many right triangles involve irrational numbers, the trig ratios for many angles are irrational. We express the irrational ratios rounded to a selected number of decimal places.

Example: Find the sine, cosine and tangent of <R. R T 30°

Answer: Sine 30° = ½ = 0. 5 Cosine 30° = √3/2 ≈0 Answer: Sine 30° = ½ = 0.5 Cosine 30° = √3/2 ≈0.866 Tangent 30° = 1/√3 ≈ 0.577

We can find the decimal values of trig ratios on a calculator We can find the decimal values of trig ratios on a calculator. For the ratios in the last example, a calculator with a square root key is sufficient. For other angles we can use the trig functions on a scientific or graphing calculator, which are often abbreviated with three letters.

Name Abbreviation Sine sin Cosine cos Tangent tan

If you have a calculator with these three keys, practice using them for the triangle in the last example. To find the sine of a 30° angle type in sin(30). The display should read 0.5. try again with that cosine and tangent of 30°. Compare the results to the last answer.

Example: Use a calculator to find the since and cosine of <A. 1 A 35°

Answer: Sine 35° = opp/hyp = 0.574/1 Cosine 35° = adj/hyp = 0.819/1

Trig ratios can help us calculate measures we cannot perform directly Trig ratios can help us calculate measures we cannot perform directly. Suppose we want to find the height of a tree. If the angle of elevation from 100 feet away is 22°, we can find the height of the tree using the tangent function.

Example: Find the height of the tree.

Answer: Tangent 22° = opp/adj = Tree height/100 feet = 0. 404/1 t = 0 Answer: Tangent 22° = opp/adj = Tree height/100 feet = 0.404/1 t = 0.404 100 1 The height of the tree is about 40.4 feet

HW: Lesson 118 #1-25