001 trig ratio defsa
TRANSCRIPT
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Drill 3/19/13•Name a ratio equal to if the triangles are similar:
ac
a
cb
f
d
e
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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.
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Objective•SW explore the sine and cosine ratios, and two of the properties associated with them.
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Right Triangle
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Greek Letters• angle theta
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Side Names in relation to • hypotenuse
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Side Names in relation to •Adjacent side (means next to)
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Side Names in relation to •Opposite side (means across
from)
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Classify the Side:
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Classify the Side:•
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Classify the Side:
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Abbreviations:
hypotenuse
(hyp.)opposite
(opp.)
Adjacent (adj.)
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Tangent Ratios:• Tangent ratio of = opp./adj.
opp.
adj.
(alpha)
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Abbreviation:• Tan = opp./adj.
opp.
adj.
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Abbreviation:• Find Tan =
3
5
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Abbreviation:• Find Tan A=
7
2 A
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Abbreviation:• Find Tan B=
7
2
B
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Abbreviation:• Find Tan =
3
5
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Abbreviation:• Find Tan =
b
a
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Calculator:• Find Tan =, if =35
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Calculator:
•Change to degree mode•Hit tan 35
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Calculator:
•Hit tan 35•Tan 35 ≈ 0.7
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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
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Abbreviation:•Find :•tan =5/3•tan-1 (tan )=
•=tan-1(5/3)=?
3
5
tan-1(5/3)
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Use a calculator:•=tan-1(5/3)=?•Hit 2nd tan (5/3)•=59.04
You must use degree mode!!
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Sine Ratios:• Sine ratio of = opp./hyp.
opp.hyp.
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Abbreviation:•Sin = opp./hyp.
opp.hyp.
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Finding Sine Ratios:• sin = ?
5
7
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Cosine Ratios:• Cosine ratio of = adj./hyp.
adj.
hyp.
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Abbreviation:• Cos = adj./hyp.
adj.
hyp.
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Finding Cosine Ratios:• cos = ?
5
7
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Calculator:• Find sin and cos , if =35
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Calculator:
•Change to degree mode•Hit sin 35
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Calculator:
•Hit sin 35•sin 35 ≈ 0.57
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Calculator:
•Change to degree mode•Hit cos 35
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Calculator:
•Hit cos 35•cos 35 ≈ 0.82
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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
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CW/HW
•Example Ex 11-1 # 1-12 and
• Example Ex. 11-2 All