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(a) Give a possible formula y = Atan(B0) +C in the following cases. 3n y 8 8 10 16 16 (b) Graph y = -tan(70) – 1 in the space below. Be sure to label vertical asymptotes and at least one 0-intercept.

(a) Give a possible formula y = Atan(B0) +C in the following cases. 3n y 8 8 10 16 16 (b) Graph y = -tan(70) – 1 in the space below. Be sure to label vertical asymptotes and at least one 0-intercept.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(a) Give a possible formula \( y = A \tan(B\theta) + C \) in the following cases. The graph depicts three tangent curves with vertical asymptotes and horizontal shifts. The vertical asymptotes are located at \( \theta = -\frac{3\pi}{16}, \theta = -\frac{\pi}{8}, \theta = \frac{\pi}{8}, \) and \( \theta = \frac{3\pi}{8} \). There are points of zero on the \(\theta\)-axis between these asymptotes. The \( y \)-intercept is at \( y = 10 \). (b) Graph \( y = -\tan\left(\frac{\pi}{4}\theta\right) - 1 \) in the space below. Be sure to label vertical asymptotes and at least one \(\theta\)-intercept.
Transcribed Image Text:(a) Give a possible formula \( y = A \tan(B\theta) + C \) in the following cases. The graph depicts three tangent curves with vertical asymptotes and horizontal shifts. The vertical asymptotes are located at \( \theta = -\frac{3\pi}{16}, \theta = -\frac{\pi}{8}, \theta = \frac{\pi}{8}, \) and \( \theta = \frac{3\pi}{8} \). There are points of zero on the \(\theta\)-axis between these asymptotes. The \( y \)-intercept is at \( y = 10 \). (b) Graph \( y = -\tan\left(\frac{\pi}{4}\theta\right) - 1 \) in the space below. Be sure to label vertical asymptotes and at least one \(\theta\)-intercept.
Expert Solution
Step 1

a) Given,

Calculus homework question answer, step 1, image 1

From the graph, we clearly see that,

Vertical shift, D=10

They are given Vertical asymptotes,

x=π8

we know,x=P2 where P is the period 

Comparing it we get,

P2=π8P=π8×2P=π4

Period=πB

π4=πBB=4ππB=4

we get,

y=Atan(4x)+10

From the graph, we get the point 3π16,5

Substitute it in the above equation we get,

5=Atan(43π16)+105-10=Atan3π4-5=A(-1)A=5

Therefore the equation becomes,

y=5tan(4x)+10

 

 

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