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anonymous
 one year ago
using complete sentences explain how to find the minimum value for each for each function and and determine which function has the smallest y value
f(x) = 3x^2 + 12x + 16
And
g(x) = 2sin (2xpi) +4
anonymous
 one year ago
using complete sentences explain how to find the minimum value for each for each function and and determine which function has the smallest y value f(x) = 3x^2 + 12x + 16 And g(x) = 2sin (2xpi) +4

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 I'm pretty sure the minimum point for f(x) is (2, 4). Is that correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep the min for f is y = 4 when x = 2 ie the min f(x) = 4 occurs at the point (2,4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay how to we find g(x)?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1when does sin(x) have a minimum?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1look at the unit circle what is the lowest point on it?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what is the corresponding angle

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'll be right back in a few minutes

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'm back no look at where it shows the angle theta

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what angle theta is where (0,1) is located?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know what it is. I'm confused

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1look at this http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024pxUnit_circle_angles_color.svg.png and tell me what the angle is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know I'm lost..

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1do you see the 270 degrees?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so that's why sin(270 degrees) = 1 or sin(3pi/2 radians) = 1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the min occurs when sin(x) = 1, ie when x = 3pi/2 so you have to determine when 2xpi is equal to 3pi/2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.12xpi = 3pi/2 what is x equal to?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you should get x = 5pi/4

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I see a shortcut though

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1they just want the min y value sin( anything ) has a min of 1 so 2sin (2xpi) +4 turns into 2*(1) +4 when you replace all of "sin..." with the smallest it can get, which is 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is confusing to me.. I'm trying to understand it but it's a lot of info.. I'm not good with trigonometry

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.12*(1) +4 turns into 2, so this is the smallest that g(x) can get

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1notice on the wavy graph, the lowest points have a y coordinate of y = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yea I noticed that. So y=2 but what is x? Do we need to know x?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1they just want to know the smallest output of the function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. So g(x) has the smallest minimum?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and you can see that on your graph you posted

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I see that now haha. Do you mind helping with one more?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Prove: \[\sin \theta\sin \theta \times \cos^2 \theta = \sin^3 \theta\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1hint: factor out sin(theta)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1only alter the left side do not change the right side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it would be \[\cos^2 \theta = \sin^3 \theta?\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you should have \[\Large \sin(\theta)\left(1\cos^2(\theta)\right) = \sin^3(\theta)\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1then try to do something with the 1sin^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would you get 1sin^2?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I meant 1cos^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would you multiply dw:1433476582158:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1there's an identity you use for 1cos^2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1hint: sin^2 + cos^2 = 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So 1cos^2 would become sin^2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait how did you get the 1 again?
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