Question

Calculus II - Average Values
[0, pi]
f(c) = f ave ->
10sin(c) - 5 sin(2c) = 20/pi
Solve for c. (Use three decimal places. There should be two answers.)

Answer 1

Was the initial question to solve 10sin(c)-5sin(2c)=10/pi ?

Answer 2

The initial question was to find the average value of 10sin(x)-5sin(x) between o and pi.
Now I need to find c such that f ave = f(c) rounded to three decimal places.

Answer 3

another dumb question is it 10sin(x)-5sin(x) or 10sin(x)-5sin(2x)

Answer 4

on an interval [a,b] of some function f the average is determined to be:\[\frac1{b-a}\int_{a}^{b}f(x)dx\]
or does memory betray me?

Answer 5

you are right

Answer 6

That's right.
It's 10sin(x)-5sin(2x).

Answer 7

I already got the f ave part right, though, so I just need to solve for c.

Answer 8

k :)

Answer 9

sin(2c) = 2sin(c)cos(c) maybe?

Answer 10

if so, factor the commons i believe

Answer 11

Trig isn't my strong point. Could you walk me through it?

Answer 12

an identity is:

sin(2x) = 2sin(x)cos(x) so replacing it gets us:

10 sin(x) - 5(2sin(x)cos(x)) = K

10 sin(x) (1 - cos(x)) = K

Answer 13

might help if we could get a ^2 going on tho

Answer 14

maybe i'm giving up too soon but i'm not seeing a good algebraic/trig approach to solve this :(

Answer 15

show me the initial function you use to find the avg

Answer 16

"The initial question was to find the average value of 10sin(x)-5sin(x) between o and pi."

you got x there is it suppsoed to be 2x?

Answer 17

f(x) = 10sin(x) - 5sin(2x)

Average value of f(x) in interval 0,pi is 20/pi

Answer 18

10sin(c) - 5 sin(2c) = 20/pi

10sin(c) - 10 sin(c) cos(c) = 20/pi

10sin(c) (1- cos(c)) = 20/pi

sin(c) - sin(c)cos(c) = 2/pi

yeah, isnt really all that workable without some fancier stuff in my eyes

Answer 19

then she wants to find the value of x at which f(x) achieves this average value

Answer 20

i would use wolfram
http://www.wolframalpha.com/input/?i=solve+10sin%28x%29-5sin%282x%29+%3D+20%2Fpi%2C+0%3Cx%3Cpi

Answer 21

can we do a newton rhapsody on f?

Answer 22

10*sin(x) -5*sin(2x) = 20/pi