7.4 TrigonometryWhat you’ll learn:

1. To find trig ratios using right triangles.

2. To solve problems using trig ratios.

Trigonometry

• Trigonometry – the study of triangle measurement

• Trigonometric Ratio – the ratio of the lengths of sides of a right triangle.

• Three most common trig ratios – sine, cosine, and tangent.

• Trig ratios are related to the acute angles of a right triangle, never the right angle.

Sine ratio

sin of A= or

sin of B= or

A

BCa

b c

OppositeHypotenuse

ac

OppositeHypotenuse

bc

Cosine Ratio

cos of A= or

cos of B= or

A

BCa

b c

AdjacentHypotenuse

AdjacentHypotenuse

bcac

Tangent Ratio

tan of A= or

tan of B= or

A

BCa

b c

OppositeAdjacent

OppositeAdjacent

abba

Writing Ratios

Find sin A, cos A, tan A, sin B, cos B, tan B. Express each ratio as a fraction and as a decimal to the nearest hundredth.

sin A= cos A= tan A=

sin B= cos B= tan B=

A

B

C

15

8

17

1517

1517

817

817

158

815

Using the calculatorScientific calculators are programmed to know what the

ratios will be for all angles. You can enter the angle and it will give you the ratio (as a decimal) or you can enter the ratio and it will give you the angle. Since we are dealing only with degrees, make sure your calculator is in “degree” mode (D or DEG should be visible)

When you are given the angle:Example: sin 50(enter sin 50 then press enter or enter 50 and press sin)

0.7660

When you are given the ratio:

To find the angle from a ratio, you must use the “second” or “shift” key to find it. (use etc..)

Ex: cos X=0.8734Enter Shift cos 0.8734 then enter or 0.8734 and

shift cosX=29.14

1cos

Finding Missing Parts. Find x to the nearest tenth.

1.

2.

3.

4.

3214

x

9X

18

46

x

16

x

7.5 15

Homeworkp. 368

18-48 even