October 16

1
October 16

• Exam III Information
• Review Session 116 Woodburn, 530 7 Thursday
• Formulas will be provided in the lab during the
  test.
• All of the basic formulas will be given.
• Some other formulas will also be given (to ensure
  that you know which to use)
• If a formula can be derived using a basic
  formula, then it might not be given.

2
Addition Subtraction of angles for Cosine Sine
3
Addition Subtraction formulas for Tangent
Not needed though. We can find the Tan(aß) by
finding Sin(aß) / Cos(aß) The same for Tan(a
ß)
4
Section 7.5 Double Angle Identities and ½ Angle
Identities
Theorem Double-Angle Formulas
The focus of Lab 6, at least for the Cosines
double angle identity.
5
Double Angle Derivation

• Sin(xx) Sin(x)Cos(x) Cos(x)Sin(x)
• 2Sin(x)Cos(x)
• Cos(xx) Cos(x)Cos(x) Sin(x)Sin(x)
• Cos2(x) Sin2(x)
• 2Cos2(x) 1
• 1 2Sin2(x)

6
13
5
-12
7
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8
What quadrant does 2? lie in?

• Review the facts
• ? was in quadrant 2.
• Sin(2?) -120/169
• Cos(2?) 119/169

• Quadrant I
• Quadrant II
• Quadrant III
• Quadrant IV
• None, 2? is a quadrantal angle

9
Derivation of ½ angle formulas
10
Derivation of ½ angle formulas
11
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12
Theorem Half-Angle Formulas
13
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14
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15
Tan(a) 4/3 a is in Quad.III

• Which of the following is correct for Sin(a / 2)
  ?
• Hint You need to figure the quadrant and also
  need the Cos(a)