Question

For the function y = -2+5sin(pi/12(x-2)), what is the maximum value?

Answer 1

what is the maximum value of 5 sin(x) for any value of x?

Answer 2

add that to -2 and you've got your answer

Answer 3

x=8+24n ?

Answer 4

wait what do i do ?

Answer 5

by the way, I'm assuming that is supposed to be interpreted as
\[y = -2 + 5\sin(\frac{\pi}{12}(x-2))\]

Answer 6

yes @whpalmer4

Answer 7

the sin function has a range of -1 to 1, right? so 5*sin has a range of 5*-1 to 5*1 = -5 to 5
So the max value of 5 sin(anything) = 5, and the max value of y will be -2 + 5 =

Answer 8

3?

Answer 9

is that an answer or a prayer? :-)

Answer 10

answer :)

Answer 11

okay!

Answer 12

hi @primeralph!

Answer 13

thank you @primeralph sorry that you felt ignored :(

Answer 14

I feel bad now :(

Answer 15

@whpalmer4 so my answer is 3 right? :)

Answer 16

so, because no restrictions were placed on the values of x, we just took the max value produced by sin(x) at any value of x, multiplied by 5, and added in the offset of -2 to get our final answer of 3 being the max.

for bonus credit, what is the minimum value of y?

Answer 17

for extra extra credit, what is the first positive value of x that gets us the max value of y :-)

Answer 18

-2?

Answer 19

nope. the range of sin(x) is -1 to 1, so the range of 5 sin(x) is -5 to 5. take the minimum value (-5) and add to the offset (-2), and you get?

Answer 20

-7 as the minimum value :)

Answer 21

here's a graph, btw

Answer 22

thanks :D

Answer 23

g2g

Answer 24

here's a better one, showing what the sine looks like without the multiplier or offset: