(a) Give a possible formula y =Atan(B0) + C in the following cases.3n37y88810-3n1616(b) Graph yone 0-intercept.-tan(70) – 1 in the space below. Be sure to label vertical asymptotes and at least=

(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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section: Chapter Questions

Problem 23T

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Question

(a) Give a possible formula y =
Atan(B0) + C in the following cases.
3n
37
y
8
8
8
10
-3n
16
16
(b) Graph y
one 0-intercept.
-tan(70) – 1 in the space below. Be sure to label vertical asymptotes and at least
=

Expert Solution

Step 1

a) Given,

From the graph, we clearly see that,

Vertical shift, D=10

They are given Vertical asymptotes,

$x = \frac{π}{8}$

we know, $x = \frac{P}{2}$ where P is the period

Comparing it we get,

$\frac{P}{2} = \frac{π}{8} P = \frac{π}{8} \times 2 P = \frac{π}{4}$

Period= $\frac{π}{|B|}$

$\frac{π}{4} = \frac{π}{|B|} |B| = \frac{4 π}{π} |B| = 4$

we get,

$y = A \tan (4 x) + 10$

From the graph, we get the point $(\frac{3 π}{16}, 5)$

Substitute it in the above equation we get,

$5 = A \tan (4 \frac{3 π}{16}) + 10 5 - 10 = A \tan (\frac{3 π}{4}) - 5 = A (- 1) A = 5$

Therefore the equation becomes,

$y = 5 \tan (4 x) + 10$

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