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3 years ago

What is the period of the function f(x)=sin(x/3) ?

Mathematics

1 answer:

vitfil [10]3 years ago

6 0

<h3>Answer: 6pi radians</h3>

(this is equivalent to 1080 degrees)

======================================

Explanation:

f(x) = sin(x/3)

is the same as

f(x) = 1*sin( (1/3)(x-0) )+0

and that is in the form

f(x) = A*sin( B(x-C) )+D

The letters A,B,C,D are explained below

A = helps find the amplitude

B = 2pi/T, where T is the period

C = determines phase shift (aka left/right shifting)

D = determines vertical shift = midline

All we care about is the value of B as that is the only thing that is connected to the period T

--------

Compare f(x) = 1*sin( (1/3)(x-0) )+0 with f(x) = A*sin( B(x-C) )+D and we see that B = 1/3, so,

B = 2pi/T

1/3 = 2pi/T

1*T = 3*2pi ... cross multiply

T = 6pi

The period is 6pi radians. This is equivalent to 1080 degrees. To convert from radians to degrees, you multiply by (180/pi).

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3 years ago

Read 2 more answers

Kate runs 2/3 of a mile on Mondays, Wednesday's and Thursdays. She runs 4/5 of a mile on Tuesday and Fridays. How many miles doe

padilas [110]

Answer:

Therefore, we conclute that Kate run 1 mile and 7/15 of a mile for the week.

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To check, we plug in our value for k into the original equation:
$5 - 6 = - 3k \\ 5 - 6 = - 3( \frac{1}{3} ) \\ - 1 = - 1$
We found k to be 1/3, so for every instance of k, we plug in 1/3. To simplify, we combine the left side to get -1, and we combine the right side to get -1.
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