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@jim_thompson5910 I'm pretty sure the minimum point for f(x) is (-2, 4). Is that correct?
yep the min for f is y = 4 when x = -2 ie the min f(x) = 4 occurs at the point (-2,4)
Okay how to we find g(x)?
when does sin(x) have a minimum?
I don't know
look at the unit circle what is the lowest point on it?
what is the corresponding angle
I'll be right back in a few minutes
(0, 1)? and okay
I'm back no look at where it shows the angle theta
what angle theta is where (0,-1) is located?
I don't know what it is. I'm confused
look at this http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1024px-Unit_circle_angles_color.svg.png and tell me what the angle is
I don't know I'm lost..
do you see the 270 degrees?
so that's why sin(270 degrees) = -1 or sin(3pi/2 radians) = -1
the min occurs when sin(x) = -1, ie when x = 3pi/2 so you have to determine when 2x-pi is equal to 3pi/2
2x-pi = 3pi/2 what is x equal to?
you should get x = 5pi/4
I see a shortcut though
they just want the min y value sin( anything ) has a min of -1 so 2sin (2x-pi) +4 turns into 2*(-1) +4 when you replace all of "sin..." with the smallest it can get, which is -1
This is confusing to me.. I'm trying to understand it but it's a lot of info.. I'm not good with trigonometry
2*(-1) +4 turns into 2, so this is the smallest that g(x) can get
notice on the wavy graph, the lowest points have a y coordinate of y = 2
Yea I noticed that. So y=2 but what is x? Do we need to know x?
they just want to know the smallest output of the function
Okay. So g(x) has the smallest minimum?
and you can see that on your graph you posted
Yeah I see that now haha. Do you mind helping with one more?
Prove: \[\sin \theta-\sin \theta \times \cos^2 \theta = \sin^3 \theta\]
hint: factor out sin(theta)
only alter the left side do not change the right side
So it would be \[\cos^2 \theta = \sin^3 \theta?\]
you should have \[\Large \sin(\theta)\left(1-\cos^2(\theta)\right) = \sin^3(\theta)\]
then try to do something with the 1-sin^2
How would you get 1-sin^2?
I meant 1-cos^2
Would you multiply |dw:1433476582158:dw|
there's an identity you use for 1-cos^2
hint: sin^2 + cos^2 = 1
So 1-cos^2 would become sin^2
Thank you so much
Wait how did you get the 1 again?