Question

how do you find the maximum for r=3+4sin(theta)?

Answer 1

by finding the 1st derivative r'=4cos(theta)
r'=0 when cos(theta)=0
theta=+-pi/2
the max will be for theta=pi/2

Answer 2

7

Answer 3

find when sin theta is max..

Answer 4

sin theta's max is 1 and minimum is -1 right? so do i multiply 4 to the one and then add 3?

Answer 5

see the attachment :)

Answer 6

wait...so is the answer pi/2 or 7..?

Answer 7

theta must be pi/2 and for theta=pi/2 the max is r(pi/2)=3+4*1=7

Answer 8

i think ans must be 7

Answer 9

because the question is to find maxima for r

Answer 10

u think theta=7?
7=r(pi/2)

Answer 11

and theta=2npi+pi/2...

Answer 12

yea ur right but i found wht should theta b then wht the max is

Answer 13

i mean..r=7

Answer 14

yea kk :)

Answer 15

and theta has multiple solution if nothing has cited about the range of theta...

Answer 16

well yea theta=2kpi+pi/2
but the angle would remain the same though

Answer 17

so if i were to find the max of r=-3+2sin theta it would be 5? sorry im still a bit confused...

Answer 18

where did the 2 come from in the -3+2=-1 ?

Answer 19

no sorry theta=pi/6

Answer 20

so the 2 is also the 2 in front of the sin in the original equation? i thought sin (pi/6) was 1/2 though..

Answer 21

ur right!!!!!!!!!!!!!! I messed it up :(

Answer 22

-3+1=-2
1 comes from 2*sin(pi/6)

Answer 23

soooo soooooorrryyyyyyyyyy :(:(:(
theta=pi/6 anyway :)

Answer 24

o no it's fine! okay so the final answer would be -2? sorry i just want to make sure... so the first thing u do is find the max of the sin theta part. and then, you find out the value of the theta that'd satisfy the max. then, multiply that sin theta value to the number in front of the sin theta in the original. then, take the first number in the original (-3) and subtract the sin thetaxfront number to get the final answer...?

Answer 25

sorry for asking so many questions! but i also want to know... in this case, r=4sin2(theta),
max of sin2theta = 1
so sin2theta=1
theta= pi/4
sin pi/4 = sq2/2
max= 0+sq2/2 = sq2/2?

i feel like i'm doing this wrong...

Answer 26

sin2theta=1
2theta=pi/2
theta=pi/4
max=4*sin2(pi/4)=4sin(pi/2)=4

Answer 27

thanks!

Answer 28

uw