Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
Continuity of Trigonometric Functions
• sin & cos are continuous everywhere.
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Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
Continuity of Trigonometric Functions
• Tangent is discontinuous wherever there are Vertical Asymptotes
– Since tan(x)= sin(x)/cos(x) , anything that would make the denominator (cos(x)) equal to zero will produce a vertical asymptote.
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Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
•
all trigonometric funcons can be disconnuous if they are in a raonal equaon. This is especially true when the trigonometric funcons occur in the denominator of a raonal equaon. In this situaon, you must solve for value of the trigonometric funcon that cause the enre denominator to equal zero.
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
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Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
Solve for all discontinuities.
f(x) = csc x
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
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Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
5
Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
6
Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
f(x) = csc x
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
7
Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
8
Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
9
Continuity and Trig.pdf
November 13, 2012
EQ: How can if find the limit of f(x) as x approaches a on a graph?
sin = y­coordinate cos = x­coordinate tan = y­coordinate / x­coordinate
10
Continuity and Trig.pdf
November 13, 2012
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