1. 8.5 and 8.6 Trigonometric Ratios

2. Agenda and Objectives Agenda Objective
Finish quiz (review first before I give it back to you)
Start notes/powerpoint on trig ratios
Classwork
Start homework
Objective
Find the sine, the cosine, and the tangent of an acute triangle.

3. Finding Trig Ratios
A trig ratio is a ratio of the lengths of two sides of a right triangle.
The word trigonometry is derived from the ancient Greek language and means measurement of triangles.
The three basic trig ratios are sine, cosine, and tangent.
Abbreviated as sin, cos, and tan respectively

4. Trigonometric Ratios
Let ∆ABC be a right triangle. The sin, the cos, and the tan of the acute angle A are defined as follows:
Side adjacent to A b
cos A = =
hypotenuse c
Side opposite A a
sin A = =
hypotenuse c
Side opposite A a
tan A = =
Side adjacent to A b

5. The famous Indian…
SOHCAHTOA Sin Cos Tan

6. Ex. 1: Find the sin, the cos, and the tan of the indicated angle.
opposite 5
sin S = ≈
0.3846
hypotenuse 13
adjacent
cosS = 12 ≈
0.9231
hypotenuse 13
opposite
tanS = 5 ≈
0.4167
adjacent 12

7. Ex. 1: Find the sin, the cos, and the tan of the indicated angle.R
opposite 12
sin R = ≈
0.9231
hypotenuse 13
adjacent
cosR= 5 ≈
0.3846
hypotenuse 13
opposite
tanR = 12 ≈
2.4
adjacent 5

8. Ex. 2: Find the sin, the cos, and the tan of 45
opposite 1 √2
sin 45= = ≈
0.7071
hypotenuse √2 2
adjacent 1 √2
cos 45= = ≈
0.7071
hypotenuse √2 2
opposite 1
tan 45=
adjacent = 1 1
You could begin by sketching the special triangle , but let’s open your book to page 311 and look it up! √2
45

9. You try: Find the sin, the cos, and the tan of 30
Triangle Book
opposite
sin 30=
hypotenuse
adjacent
cos 30=
hypotenuse
opposite
tan 30=
adjacent
First try using the triangle at the right to figure out the measure. Then compare your answers to the table on page 311.
30 √3

10. Ex: 5 Using a Calculator
You can use a calculator to approximate the sin, cos, and the tan of 74. Make sure that your calculator is in degree mode.
The following table shows some sample keystroke sequences accepted by most calculators.

11. Sample keystrokes

12. More examples

13. Independent Practice Page 306 1-7 Page 313 1-7 HOMEWORK
Page even
page even