001 trig ratio defsa

Drill 3/19/13•Name a ratio equal to if the triangles are similar:

ac

a

cb

f

d

e

Objective• STW learn the vocabulary

relating angles to sides in right triangles for trigonometry

• STW explore the sine and cosine ratios, and two of the properties associated with them.

Objective•SW explore the sine and cosine ratios, and two of the properties associated with them.

Right Triangle

Greek Letters• angle theta

Side Names in relation to • hypotenuse

Side Names in relation to •Adjacent side (means next to)

Side Names in relation to •Opposite side (means across

from)

Classify the Side:

Classify the Side:•

Classify the Side:

Abbreviations:

hypotenuse

(hyp.)opposite

(opp.)

Adjacent (adj.)

Tangent Ratios:• Tangent ratio of = opp./adj.

opp.

adj.

(alpha)

Abbreviation:• Tan = opp./adj.

opp.

adj.

Abbreviation:• Find Tan =

3

5

Abbreviation:• Find Tan A=

7

2 A

Abbreviation:• Find Tan B=

7

2

B

Abbreviation:• Find Tan =

3

5

Abbreviation:• Find Tan =

b

a

Calculator:• Find Tan =, if =35

Calculator:

•Change to degree mode•Hit tan 35

Calculator:

•Hit tan 35•Tan 35 ≈ 0.7

Inverse Tangent:• If Tan =opp/adj, then the inverse tangent, abbreviated tan-1 (also referred to as arctan) is used to find the angle, when given the sides

Abbreviation:•Find :•tan =5/3•tan-1 (tan )=

•=tan-1(5/3)=?

3

5

tan-1(5/3)

Use a calculator:•=tan-1(5/3)=?•Hit 2nd tan (5/3)•=59.04

You must use degree mode!!

Sine Ratios:• Sine ratio of = opp./hyp.

opp.hyp.

Abbreviation:•Sin = opp./hyp.

opp.hyp.

Finding Sine Ratios:• sin = ?

5

7

Cosine Ratios:• Cosine ratio of = adj./hyp.

adj.

hyp.

Abbreviation:• Cos = adj./hyp.

adj.

hyp.

Finding Cosine Ratios:• cos = ?

5

7

Calculator:• Find sin and cos , if =35

Calculator:

•Change to degree mode•Hit sin 35

Calculator:

•Hit sin 35•sin 35 ≈ 0.57

Calculator:

•Change to degree mode•Hit cos 35

Calculator:

•Hit cos 35•cos 35 ≈ 0.82

Inverse sine and cosine:• If sin =opp/hyp and cos =adj/hyp, then the inverse sin and cos, abbreviated sin-1 and cos-1 (also referred to as arcsin and arccos) is used to find the angle, when given the sides

CW/HW

•Example Ex 11-1 # 1-12 and

• Example Ex. 11-2 All