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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?

(0, -1)?

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

I don't know I'm lost..

do you see the 270 degrees?

Yes

so that's why sin(270 degrees) = -1
or sin(3pi/2 radians) = -1

2x-pi = 3pi/2
what is x equal to?

0?

you should get x = 5pi/4

I see a shortcut though

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?

yes

and you can see that on your graph you posted

Yeah I see that now haha. Do you mind helping with one more?

alright

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?

oops

I meant 1-cos^2

Would you multiply |dw:1433476582158:dw|

nope

there's an identity you use for 1-cos^2

hint: sin^2 + cos^2 = 1

So 1-cos^2 would become sin^2

yep

Thank you so much

you're welcome

Wait how did you get the 1 again?