Download Trigonometric Identities

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Trigonometric Identities
Unit 5C Day 4
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Do Now
a standard-position angle θ drawn in the unit
circle, find the following:
 Given
sinθ
 cosθ
 tanθ
 cscθ
 secθ
 cotθ

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Identities
 An
identity is an equation of two functions that is
always true for every possible input value.

You already know some trigonometric identities: the
reciprocal identities.

Cosecant is the reciprocal of ________, so cscθ= ______.

Secant is the reciprocal of ________, so secθ= ______.

Cotangent is the reciprocal of ________, so cotθ= ______.
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Trigonometric Functions of Any
Angle
 Earlier, we
discovered that for
an angle θ, its terminal point
on the unit circle is
(________, ________)
 We
also discovered a new
identity: a quotient identity
 tanθ= _________

Therefore, cotθ= ____________
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Quotient Identities
 Remember
that dividing by a fraction is the
same as ____________________________
 Ex:
 Ex.:
1
3
¸
=
2 2
3 1
¸ =
2 2
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Sine and Cosine
 Use
(cosθ, sinθ)
the unit circle to find the following values:
1.
sin(150º)
2.
cos(225º)
3.
sin(300º)
4.
cos(210º)
5.
sin(135º)
6.
cos(330º)
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Using Identities
 Use
(cosθ, sinθ)
the unit circle to find the following values:
1.
tan(150º)
2.
csc(225º)
3.
sec(300º)
4.
cot(210º)
5.
tan(135º)
6.
sec(330º)
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Quadrantal Angles
(cosθ, sinθ)
 Use the unit circle to find the following values:
1.
sin(180º)
2.
cos(0º)
3.
sin(270º)
4.
tan(90º)
5.
tan(360º)
6.
sec(180º)
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Closure
 State
the three reciprocal trigonometric identities.
 State
the two quotient trigonometric identities.