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How to divide sin?by NanoPassion
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#1
May211, 04:06 PM

P: 1,306

1. The problem statement, all variables and given/known data
Its a word problem but I will just state everything here in simple form. Given  V initial = 100ft/s r=300ft r= 1/32 V^2 Sin 2theta Unknown  Solve for theta 3. The attempt at a solution 300=1/32 (100)^2 sin 2theta 300= 1/32 (10000) sin 2theta 300= 312.5 sin 2theta 300/312.5= sin 2theta .96 = sin 2theta I know the next step would be to divide by sin but how??? 


#2
May211, 04:20 PM

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P: 21,215

If you have a variable that is the argument to a function, what can you do to get at the function's argument? 


#4
May211, 04:24 PM

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HW Helper
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P: 26,157

How to divide sin?
(have a theta: θ and try using the X^{2} tag just above the Reply box )



#5
May211, 04:57 PM

P: 1,306

f(2x)=.96 2x=.96 x=.48??? .grrr I'm having a little trouble =/ I can't seem to get the inverse .. What I did before was I asked myself: sin of what? = .96 < plugged it in calculator as sin of inverse =/ 2θ = 1.287 θ = .6435 But I want to figure our whats going on in between. And is there a button here for theta? 


#6
May211, 04:58 PM

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#7
May211, 04:59 PM

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If you have sinx = A, then x = sin^{1}(A).



#8
May211, 05:07 PM

P: 1,306

I'm used to things such as: f(x) = 2x+4 y = 2x+4 y/2 2 = x f^{1}x = 1/2y  2 but when it comes to f(2x) = .96 then I'm confused on what to do. 


#9
May211, 05:17 PM

P: 15

Isn't sin2[tex]\theta[/tex] a trigonometric Identity that becomes 2 sin [tex]\theta[/tex] cos[tex]\theta[/tex]?



#10
May211, 05:21 PM

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P: 21,215

In your problem, the function is the sine function, and your equation is:
sin(2x) = .96 (I'm using x instead of theta.) The thing to do is to apply the inverse sin function to both sides. sin^{1}(sin(2x)) = sin^{1}(.96) ==> 2x = sin^{1}(.96) ==> x = (1/2)sin^{1}(.96) This will give you one value for x, but it might be that your problem calls for other solutions. If so, you will need to use some of the ideas from trig to get the other solutions. 


#11
May211, 05:23 PM

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P: 21,215

and this doesn't get you closer to a solution. Using inverse functions does. 


#12
May211, 05:44 PM

P: 1,306

My question is, how does sin^{1} cancel with sin when you multiply them together? It doesn't sound mathematically logical? I need the steps in between. 


#13
May211, 06:04 PM

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P: 21,215

One thing that you need to understand here is that the operation is NOT multiplication. This is something you have not been clear on since your first post in this thread. sin(2x) is sometimes written as sin 2x. In either form it is NOT sin times 2x  it's sin of 2x. Similar to what I wrote earlier  f(2x) is not f times 2x. It's f OF 2x, where f was the name of some unspecified function. For example, if f(x) = 2x + 3, then the inverse of this function is f^{1}(x) = (x  3)/2. f(f^{1}(2) = 2 and f^{1}(f(0)) = 0. You can verify these statements by using the formulas for the functions. In a similar way sin(sin^{1}(x) = x, but there are some restrictions of the values of x that are allowed. Also, in the opposite order, sin^{1}(sin(x)) = x, and there are some restrictions here, as well. In the first equation, x has to be between 1 and +1, inclusive. In the second equation, x has to be between pi/2 and +pi/2 if you're working in radians, or between 90 deg and +90 deg, if you're working in degrees. 


#14
May211, 06:06 PM

P: 163

Yes, sin1(sin(theta) ) = theta



#15
May211, 06:10 PM

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P: 1,347

For instance, what is [tex]\sin^{1} (\sin 3\pi/4)[/tex] ? Hint: it's not 3π/4. 


#16
May211, 06:17 PM

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#17
May211, 06:18 PM

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Do they still teach English students how to diagram sentences? If you've seen that, there's a similar thing for mathematical expressions.
The diagram (which can called a "parse tree") for the expression 2x+1 would be:
Functions, such as sin are like + and * and other operations. The diagram for the expression sin 2xlooks like
arcsin sin 2xit would be



#18
May211, 06:33 PM

P: 163

Oops... forgot about the range of theta this IS true for, as noted by Mark44.



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