Pythagorean Identity - file · Web viewChapter 11C | p. 265. Trigonometric Relationships....
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Chapter 11 | Trig Equations and Identities Chapter 11C | p. 265 Trigonometric Relationships Chapter 11D | p. 270 Double Angle Formulae NOTE Pay attention to restrictions given o Fix negative values to positive if necessary If word problem asking for interval above a value, use the CAST diagram to Reciprocal Identities cscθ= 1 sin θ secθ= 1 cos θ cot θ= 1 tan θ Pythagorean Identity sin 2 θ+ cos 2 θ= 1 Quotient Identities tan θ= sin θ cos θ cot θ= cos θ sin θ tan2 θ= 2tan θ 1−tan 2 θ sin2 θ=2 sin θ cos θ cos2 θ=cos 2 θ−sin 2 θ cos2 θ=1−2sin 2 θ cos2 θ=2 cos 2 θ−1
Transcript of Pythagorean Identity - file · Web viewChapter 11C | p. 265. Trigonometric Relationships....
Chapter 11 | Trig Equations and IdentitiesChapter 11C | p. 265
Trigonometric Relationships
Chapter 11D | p. 270
Double Angle Formulae
NOTE Pay attention to restrictions given
o Fix negative values to positive if necessary If word problem asking for interval above a value,
use the CAST diagram to determine the angles it must be BETWEEN (it is not greater than both angles, it’s greater than the smaller one and smaller than the greater one)
CALCULATE other possible values for the θ by adding to the ANGLE not the “x”
o OR you can modify the interval to account for the transformations to the θ
Use LS = RS Consider the θ separately can temporarily replace it if it’s an expression
with a variable
Reciprocal Identitiescsc θ= 1
sin θ
secθ= 1cosθ
cot θ= 1tan θ
Pythagorean Identitysin2θ+cos2θ=1
Quotient Identitiestanθ= sin θ
cosθ
cot θ=cos θsinθ
tan2θ= 2 tanθ1−tan2θ
sin 2θ=2sin θ cosθ
cos2θ=cos2θ−sin2θcos2θ=1−2 sin2θcos2θ=2cos2θ−1
