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Trigonometric Identities
Reciprocal
1. cscθ =
2. secθ = 3. cotθ =
Find all values of θ in [0,2π] given sec θ = 1.25.
Quotient
1. tanθ =
2. cotθ =
Pythagorean Identities
Use pythagorean identities to solve...
Equation of the unit circle
x2 + y2 = 1
1. If cot x =1/3 and cosx < 0, find the value of secx and cosx.
cos2θ + sin2θ = 1
1 + tan2θ= sec2θ
cot2θ + 1 = csc2θ
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Practice:
2. a) Find sin x and cos x if tan x = 4 and sin x > 0.
February 13, 2012
Symmetry Relationships
Recall: odd f(­x) = ­f(x)
even f(­x) = f(x)
1. sin(­x)=­sinx
csc(­x)=­cscx
2. cos(­x)=cosx
sec(­x)=secx
3. tan(­x)=­tanx
cot(­x)=­cot x
Write an equivalent expression
1. tan(­x)cos(­x)
Cofunctions
sin30=cos60
cofunctions are = if their angles add to 90
2. cot(­x)csc(­x)
1. sinθ =cos(π/2­θ)
2. secθ =csc(π/2­θ)
3. tanθ =cot(π/2­θ)
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5.1.notebook
February 13, 2012
ex. if cos x = .34, find sin(π/2­x)
ex. Simplify: sin(π/2­x)cscx
ex. if cos x = .34, find sin(x ­π/2)
ex. Simplify: (1 + sinx)2 + 1/sec2x
ex. Show tanx + cotx = secxcscx
Journal: Why does sin(­x) = ­sin x?
ex. if cos x = .34, find sin(x ­π/2)
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February 13, 2012
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