20 Days. Three days Graphing Sine and Cosine WS.
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Transcript of 20 Days. Three days Graphing Sine and Cosine WS.
Theorem on Amplitude, Periods, and Phase Shifts
20
:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)
.b
c- isshift phase theand ,
2 is period the, is amplitude the(1)
: thenb, and a numbers real nonzerofor )cos(or )sin( If
cbx
ba
cbxaycbxay
Reminder: Theorem on Amplitude, Periods, and Phase Shifts
20
:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)
.b
c- isshift phase theand ,
2 is period the, is amplitude the(1)
: thenb, and a numbers real nonzerofor )cos(or )sin( If
cbx
ba
cbxaycbxay
At what angles is the tangent function undefined?
What about the cotangent?
What do you think will be in our graph at those points?
Graphing Tangent and Cotangent
Theorem on Amplitude, Periods, and Phase Shifts
2
2
:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)
.b
c- isshift phase theand , is period the(1)
: thenb, and a numbers real nonzerofor )tan( If
cbx
b
cbxay
cbx
b
cbxay
0
:inequality thesolvingby found becan cycle oneexactly containing intervalan (2)
.b
c- isshift phase theand , is period the(1)
: thenb, and a numbers real nonzerofor )cot( If
Definition of the Inverse Sine Function
22 and 11for
sin ifonly and if sin
by definded is arcsin,or sin denoted function, sine inverse The
1
1
yx
yxxy
Definition of the Inverse Cosine Function
yx
yxxy
0 and 11for
cos ifonly and if cos
by definded is arccos,or cos denoted function, cosine inverse The
1
1
Definition of the Inverse Tangent Function or Arctangent Function
.22
andnumber x realany for
tan ifonly and if tan
by definded is arctan,or tandenoted function, tangent inverse The
1
1
y
yxxy
http://etc.usf.edu/clipart/galleries/672-trigonometry-graphs