Help with work

kwinrow · 2008-07-30 03:09:18

Basically i am stuck:

1.) cos(arctan(3/u))

my work:

theta=arctan(3/u)
tan(theta)=3/u

now what do i do?

2.) theta=2arcsin(1/1.2)

my work:

divided 1.2 into 1 and got:

theta= 2(.9851107833)

then do i multiply 2 into .9851107833?

am i doing this right?

John E. Franklin · 2008-07-30 03:36:01

for 1.), visualize a stairway where the steps are "u" sized for your shoe length when walking up the stairs.
And the height of the stairs is 3. But the height of a "unit" stairway (like a unit circle), is 1 for each step.
So scale down the staircase three times smaller, the opposite of the grinch's heart expansion.
This reveals a step that is "u/3" for the shoe length, which is your answer because the
cosine, huh woops, actually, your have to divide the shoelength by the hypotenuse, almost forgot,
because the hypotenuse from between the corners of the staircase must be 1, not the height of
the stairs, soory, let's start again...
take2 1.) dy = 3 ; dx = u (rise over run stuff) hypotenuse = sqrt(uTuP3T3), where T is multiply and P is add.
Now cosine = dx/hypoten., which is u/sqrt(uTuP3T3), or (u^2/[u^2+9])^(1/2)
Am I right?

John E. Franklin · 2008-07-30 03:48:05

for 2.) you are in radians, not degrees, but yes you are right.
These are 2 answers before you double it for final answer:
180 - ((arcsin(1 / 1.2) / pi) * 180) = 123.55731 degreez (2nd quadrant answer)
(arcsin(1 / 1.2) / pi) * 180 = 56.4426902 degreez = (1st quadrant answer)
Also can add 360 or -360 any number of times to above answers before doubling.

kwinrow · 2008-07-30 03:51:07

i was following the formula in the book and your answer is very similar to the format they used. This is what I got for my final answer:

3sqrt(u^2+1)/(u+1)

John E. Franklin · 2008-07-30 03:54:22

arcsin(1 / 1.2) = 0.985110783 (Then just add or subtract 2pi as many times as want and double it for answer)
pi - arcsin(1 / 1.2) = 2.15648187 (This one I measured going up from the leftward vector (west direction)-- that's why I subtracted from pi radians which is 180 degrees, but I haven't doubled it yet or put in the 360 cycle-adders)
pi / 2 = 1.57079633 (this is the vertical 90 degree mark)

kwinrow · 2008-07-30 04:00:03

i confused why do u keep stating add or subtract 360 or 2pi any number of times

John E. Franklin · 2008-07-30 04:10:18

no one ever taught you that? for an angle, it has an east leg and a north leg, and if you
go around the circle, around and around, you still end up at the same angle, see?
Like in the olympics, they spin around and do 360's 540's, 720's=2 turns
900's=2 1/2 turns
1080's=3 turns
1260's=3 1/2 turns

kwinrow · 2008-07-30 04:18:08

ok so this is what i am getting form you:

(in degrees)

arcsin(1/1.2)=56.44269024

now from here can i just go ahead and multiply the 2 or do I have to do something else first?

this is where i am confused

John E. Franklin · 2008-07-30 04:30:58

Yes, you can double that and that will be one of the possible answers.
Should be about 112.885 degrees.

There is another answer that is over to the left when the windshield wipers goe to the left.
the 56.44 degrees in the windshield wipers to the right.
Because "sin" you just have to memorize is Upward either on the left or the right, and also
divided by 1, if the hypotenuse is 1.

kwinrow · 2008-07-30 04:37:13

ok thanks a lot just needed clarification.

John E. Franklin · 2008-07-30 04:46:04

Glad to help a little bit. I've got nothing better to do until I go get some groceries.

Math Is Fun Forum

#1 2008-07-30 03:09:18

Help with work

#2 2008-07-30 03:36:01

Re: Help with work

#3 2008-07-30 03:48:05

Re: Help with work

#4 2008-07-30 03:51:07

Re: Help with work

#5 2008-07-30 03:54:22

Re: Help with work

#6 2008-07-30 04:00:03

Re: Help with work

#7 2008-07-30 04:10:18

Re: Help with work

#8 2008-07-30 04:18:08

Re: Help with work

#9 2008-07-30 04:30:58

Re: Help with work

#10 2008-07-30 04:37:13

Re: Help with work

#11 2008-07-30 04:46:04

Re: Help with work

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