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a. Drill 3/15/12. c. Name a ratio equal to if the triangles are similar: . f. e. c. b. a. d. 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. - PowerPoint PPT Presentation
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Drill 3/15/12•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 All
