SECT. 3.8 GRAPHING THETANGENT FUNCTION
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TANGENT FUNCTION
The Tangent function is like a reciprocal function
At points where cosθ = 0, you will get a vertical asymptotebecause the reciprocal of zero Undefined
At points where sinθ = 0, you will be a x-intercept
At points where sinθ = cosθ , the value of tanθ will beequal to 1 (ie: 45°, 135°, 225°, and 315°, reference angleequals 45°)
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x
y
-3
-2
-1
1
2
3
TANGENT FUNCTION
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x
y
-2
2
The tangent function can be defined as the y-coordinate ofthe extension of the terminal arm on a vertical tangent line
As the angle changes and increase, the value of tanθ willfluctuate from negative to positive infinity
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Ex: Indicate the following for the tangent function:
a)Domain & Range
b)X-intercepts and the general formula
c)Period and amplitude
x
y
-3
-2
-1
1
2
3
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VERTICAL ASYMPTOTE AND GENERAL FORMULA:
Since tanθ = (sinθ/cosθ), the vertical asymptotes will allappear when cosθ=0 (Denominator is equal to zero)
The general formula for all the vertical asymptotes in atangent function will be:
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Ex: Given that 0< θ< 2π , tanθ > 0 and sinθ < 0, whatquadrant is the angle in?
If tanθ > 0 (positive), then it can only be in quadrants 1 and 3
If sinθ < 0 (negative), then it can only be in quadrants 2 and 3
To satisfy both conditions, then the angle must be in quadrant 3