Radius of Circle of which Angle of 3 Radiants Cutts off An Arc of 45 CM | Mathematics | Page 1

eager mulch Nov 10, 2022, 8:02 PM

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What is the radius of a circle in which an angle of 3 radians cuts off an arc of 45 cm?

I don't understand what it wants.

fiery wedge Nov 10, 2022, 8:52 PM

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3 rad is the arc length
2πr=full circumference
(3/(2π))×2πr=45
(6πr)/2π=3r=45
r=15

It all makes sense to me, but if it's incorrect then I could actually spend some time on it

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@eager mulch

eager mulch Nov 10, 2022, 8:53 PM

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fiery wedge 3 rad is the arc length 2πr=full circumference (3/(2π))×2πr=45 (6πr)/2π=3r=45 r=...

yeah i was able to figure it out, ty tho for confirming im not insane

waxen mangoBOT Nov 10, 2022, 8:53 PM

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@eager mulch has given 1 rep to @fiery wedge

fiery wedge Nov 10, 2022, 8:53 PM

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thank you

eager mulch Nov 10, 2022, 8:53 PM

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Do you happen to know how to find sec theta

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fiery wedge Nov 10, 2022, 8:56 PM

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sec=1/cosθ
cotθ=(cosθ)/(sinθ)
arccot(2)=θ

1/cos(arccot(2))=√5/2

eager mulch Nov 10, 2022, 9:01 PM

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fiery wedge sec=1/cosθ cotθ=(cosθ)/(sinθ) arccot(2)=θ 1/cos(arccot(2))=√5/2

What would I do for this one? It is similar but uses tangent, wouldn't it be like sqrt(1 + x^2)/x

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Or am I wrong

fiery wedge Nov 10, 2022, 9:04 PM

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tan would be (x)/(√(1-x²))

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cos=√(1-x²)

eager mulch Nov 10, 2022, 9:09 PM

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fiery wedge tan would be (x)/(√(1-x²))

Ok cool so I did get it right

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Then, would you happen to know how to solve this? I got -1

fiery wedge Nov 10, 2022, 9:10 PM

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tan(15) would give you the slope of that line, the negative reciprocal of that would give you the slope of the original line

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-1/tan(15) would be the slope

eager mulch Nov 10, 2022, 9:11 PM

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So -3.732

fiery wedge Nov 10, 2022, 9:11 PM

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seems it

eager mulch Nov 10, 2022, 9:11 PM

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For this, it would be 4x + 9, right

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Since p(2x + 3) = 2(2x + 3) + 3

fiery wedge Nov 10, 2022, 9:12 PM

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yes

eager mulch Nov 10, 2022, 9:12 PM

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And for this, z = 3e^(i(pi/2)), right

fiery wedge Nov 10, 2022, 9:12 PM

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which year are you in university? these questions seem odd

eager mulch Nov 10, 2022, 9:12 PM

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I am learning pre calculus

fiery wedge Nov 10, 2022, 9:12 PM

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so not in Uni?

eager mulch Nov 10, 2022, 9:13 PM

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No, but these questions are weird

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We have multiple choice practice flyers we are given

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So we can make sure we're up to snuff for a test

fiery wedge Nov 10, 2022, 9:13 PM

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eager mulch And for this, z = 3e^(i(pi/2)), right

-3e^(iπ/2)
3e^(i3π/2)

eager mulch Nov 10, 2022, 9:14 PM

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eager mulch And for this, z = 3e^(i(pi/2)), right

Like for this question, the possible answers are:

z = e^i3pi/2
z = 3e^i3pi/2
z = 3e^ipi/2
z = epi/3

fiery wedge Nov 10, 2022, 9:15 PM

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yeah my bad for the 3π/4

eager mulch Nov 10, 2022, 9:15 PM

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Yeah, thought so

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Since that would be a very odd number for the type of problem

fiery wedge Nov 10, 2022, 9:15 PM

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3e^ipi/2 would be 3i

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have to go ¾ around or π/2 clockwise

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so -π/2

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2 solutions in 1 rotation, infinite solutions otherwise

eager mulch Nov 10, 2022, 9:17 PM

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Yeah ok that makes sense

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I was just being dumb 💀

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So, I have one more question that I don't understand entirely.

fiery wedge Nov 10, 2022, 9:18 PM

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3e^i3π/2
3e^-iπ/2
-3e^iπ/2
-3e^-3iπ/2

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2=4sinθ
0.5=sinθ

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you can then do arcsin

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θ=π/6,30°

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asks for answer in radians

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so just π/6

eager mulch Nov 10, 2022, 9:21 PM

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Is the amplitude of something always positive

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Like y = -2 cos t + 3

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Would amplitude be -2 or 2

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Or either

fiery wedge Nov 10, 2022, 9:22 PM

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amplitude in what context?

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physics?

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amplitude in physics is always positive

eager mulch Nov 10, 2022, 9:23 PM

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amplitude in precalc

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for a trig function

fiery wedge Nov 10, 2022, 9:23 PM

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always positive

eager mulch Nov 10, 2022, 9:23 PM

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Ok thought so

#Radius of Circle of which Angle of 3 Radiants Cutts off An Arc of 45 CM