Trig problem :(
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| Find the value of s in the interval [0, π/2] that makes the statement true. cot s = 7.25754565 |
I'm stuck here. I've gone about this multiple ways and can't get the right answer. Got any tips on how to do this?
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And what is the problem, exactly? Also, what's the value of n in this example? Not that it matters, though as I don't think there's any degrees of liberty here to play with.
The cotangent is defined as 1 / tangent. That means all you need to do is calculate the hyperbolic tangent of the inverse of the right-hand side. See http://a.ly/5Zf .
Or am I missing something here?
The cotangent is defined as 1 / tangent. That means all you need to do is calculate the hyperbolic tangent of the inverse of the right-hand side. See http://a.ly/5Zf .
Or am I missing something here?
cot s = x
1 / tan s = x
tan s = 1/x
s = arctan (1/x)
So:
s = arctan (1/7.25754565) = 0.136925442... by calculator (make sure in radians mode, not degrees mode)
And: 0 < 0.136925442... < (pi / 2)
So we're done.
1 / tan s = x
tan s = 1/x
s = arctan (1/x)
So:
s = arctan (1/7.25754565) = 0.136925442... by calculator (make sure in radians mode, not degrees mode)
And: 0 < 0.136925442... < (pi / 2)
So we're done.
Surely you can just use cot-1? Or is there not an inverse cot function? (I was never taught cot, sec or csc).
Yes, arctangent. I haven't done trig for so long I confused the two. Oh and that was PI/2. I thought it was an 'n'.
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Cool that worked :D I guess I was overthinking it, was having troubles getting cot^-1 on my calculator since I have no cot button.
Got another for you, word problem this time. I have the answer to this one, but no idea how to get there. Any guidance would be great
Got another for you, word problem this time. I have the answer to this one, but no idea how to get there. Any guidance would be great
| A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the frequency of the system is (5/pi) cycles per second, determine a trigonometric model that gives the position of the weight at time t second. |
That would be obtained by resolving the differential equation of the balance of forces. It should yield a sineful equation, probably something along 3sin(...) or 3cos(...).
Yea I've figured that much. The answer is actually
But I don't understand the 10t part
| y = -3cos * 10t |
But I don't understand the 10t part
The minus sign for the "3" is simply due to axis convention: Anything below the equilibrium is negative.
What's the argument of the cos() function?
But in any case, to arrive to the equation, you must write down the balance of forces for any given time t. This will give you a differential equation that must be resolved. By resolving it you arrive to the final equation.
EDIT: Just so you know, I ask about the argument to cos() because your shown answer is not correct. I bet it is most likely a typo. It doesn't have physical meaning: The amplitude cannot possible increase as time increases. I an ideal model, the amplitude never decreses, but never increases beyond its maximum value; in a more realistic model (one that would include frictional forces), the amplitude is bound to decrease as time increases.
What's the argument of the cos() function?
But in any case, to arrive to the equation, you must write down the balance of forces for any given time t. This will give you a differential equation that must be resolved. By resolving it you arrive to the final equation.
EDIT: Just so you know, I ask about the argument to cos() because your shown answer is not correct. I bet it is most likely a typo. It doesn't have physical meaning: The amplitude cannot possible increase as time increases. I an ideal model, the amplitude never decreses, but never increases beyond its maximum value; in a more realistic model (one that would include frictional forces), the amplitude is bound to decrease as time increases.
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Ah sorry that was a typo. The answer is
This, I do not understand. I have a feeling you're using some calculus terms (or trig terms I've yet to get into), and I haven't taken calculus yet. I'm trig as a prerequisite to calc. The extent of my college math is college algebra and discrete math. :/
| y = -3cos(10t) |
| But in any case, to arrive to the equation, you must write down the balance of forces for any given time t. This will give you a differential equation that must be resolved. By resolving it you arrive to the final equation. |
This, I do not understand. I have a feeling you're using some calculus terms (or trig terms I've yet to get into), and I haven't taken calculus yet. I'm trig as a prerequisite to calc. The extent of my college math is college algebra and discrete math. :/
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Yeah, this is definitely a problem that requires calculus to solve. In fact, I never solved these kinds of problems until DQ. It does seem strange that you would be tackling them in a trig class before taking calculus.
In any case, maybe this can help to visualize the solution:
http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html
In any case, maybe this can help to visualize the solution:
http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html
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You just need to know that the behaviour is a sine. (that's data in a lot of problem)
x(t) = A \sin(\omega t + \phi)
\omega = 2 \pi f
The problem description gives you 'A' and 'f'.
You can get the phase by doing x(0) = -3
x(t) = A \sin(\omega t + \phi)
\omega = 2 \pi f
The problem description gives you 'A' and 'f'.
You can get the phase by doing x(0) = -3
Yea I'm not sure why we're doing this before calc then. My university does things weird. I hear people normally take discrete math after most of their other math classes, yet it was my first real math class here (I dont count college algebra). And we have two semesters of discrete :/
Again, you don't need calculus to solve that problem.
The plan is like that for a reason. If you think that the objectives are not met, complain and you may change it.
Sadly, it would probably be too late for you.
The plan is like that for a reason. If you think that the objectives are not met, complain and you may change it.
Sadly, it would probably be too late for you.
Ne555 is right, you should use your knowledge of the behaviour of the function to deduce the solution. Not sure what "Sadly, it would probably be too late for you." means though...
EDIT: A lot of calculus being mentioned here, it would be wasted on this problem considering this course probably hopes you know the equations that govern simple harmonic motion. The alternative is a simple but tedious 2nd order differential equation I believe.
EDIT: A lot of calculus being mentioned here, it would be wasted on this problem considering this course probably hopes you know the equations that govern simple harmonic motion. The alternative is a simple but tedious 2nd order differential equation I believe.
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Which also assumes that you know that the solution is A_k \exp( \lambda_k )
What I tried to say was that the change would start after him.
What I tried to say was that the change would start after him.
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