Download 4.5 Graphs of tan cot sec csc comp.notebook

4.5 Graphs of tan cot sec csc comp.notebook
January 08, 2016
4.5 Graphs of Cscx, Secx,Tanx, and Cotx
The Cosecant Function
cscx=
cscx=1 when Domain
Range
Period
Vertical asymptotes of cscx are zeros of
Dec 30­8:50 PM
4.5 Graphs of tan cot sec csc comp.notebook
January 08, 2016
The Secant Function
secx=
secx =1 when Domain
Range
Period
Vertical asymptotes of secx are zeros of
Dec 30­8:50 PM
4.5 Graphs of tan cot sec csc comp.notebook
January 08, 2016
The Tangent Function
tanx=
Domain
Range
Period
Zeros of tanx are zeros of
Vertical asymptotes of tanx are zeros of
Dec 30­8:50 PM
4.5 Graphs of tan cot sec csc comp.notebook
January 08, 2016
The Cotangent Function
cotx=
Domain
Range
Period
Zeros of cotx are zeros of
Vertical asymptotes of cotx are zeros of
Ex. 1
Describe the transformation from y=tanx to f(x)=tan2x and sketch 2 periods.
TRY
Describe the transformation from y=secx to f(x)=­2sec3x and sketch 2 periods.
Dec 30­8:50 PM
4.5 Graphs of tan cot sec csc comp.notebook
Solving a Trig Equation Algebraically
Ex.1 Solve for x, tanx=­1 for π ≤ x ≤ π
2
Solution:
Which quadrant is it in? Draw a reference triangle.
Ex.2 Solve for x, cscx=­2 for π ≤ x ≤ 2π
Dec 30­8:50 PM
January 08, 2016
4.5 Graphs of tan cot sec csc comp.notebook
Solving a Trig Equation Graphically
Ex.3 Find the smallest positive number such that 2x=secx.
Solution: Graph both equations and look for intersection.
Dec 30­8:50 PM
January 08, 2016