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sin (0.77x) = 1/2
How did they get 0.77x = 3.665 and 5.760?
Someone please help show me the steps of their work so I can see it.
 one year ago
 one year ago
sin (0.77x) = 1/2 How did they get 0.77x = 3.665 and 5.760? Someone please help show me the steps of their work so I can see it.
 one year ago
 one year ago

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theEricBest ResponseYou've already chosen the best response.1
I think there are two ways. The first is memorizing what you take the sine of to get 1/2. The other ways is using the inverse sine function. Because\[sin(77x)=\frac{1}{2}\], you can say \[77x = sin^{1}(\frac{1}{2})\]
 one year ago

theEricBest ResponseYou've already chosen the best response.1
This only helps if you have a calculator..
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
Hello, thank you for answering. This is what I initially thought as well. however, the inverse sine of negative one half gave me: 0.5235987756 radians. Above it shows different answers for the solution.
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
So I am baffled how my text came up with such a number.
 one year ago

theEricBest ResponseYou've already chosen the best response.1
Huh! I'm foggy on trigonometry, sorry!
 one year ago

theEricBest ResponseYou've already chosen the best response.1
I used wolfram alpha to solve for \[a\]in\[sin(a)=\frac{1}{2}\] and it produced \[x=\frac{7\pi}{6}+2\pi n_1\]and\[x=\frac{11\pi}{6}+2\pi n_2\]
 one year ago

theEricBest ResponseYou've already chosen the best response.1
The first is 3.6651914291880921115397506138260866982300309659376234...
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
Oh I see.. The 3.665 and 5.760 are just decimal equivalents of the fraction. Thanks for shedding some light on it.
 one year ago

theEricBest ResponseYou've already chosen the best response.1
If you got it, then congratulations! I'm still a bit confused! :)
 one year ago

theEricBest ResponseYou've already chosen the best response.1
The second resolves to 5.7595865315812876038481795360124219543614772321876940... when \[n_2=0\]
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
Haha. I got it. It is saying. The sine function is equal to 1/2 in two different quadrants. In a circle (degrees) it is located at 7pi/6 and 11pi/6 These are equivalent to a 30 degree angle (pi/6) in the first quadrant. 7pi/6 = 3.665
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
Excuse me, those are radians!
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
Well thanks for guiding me. I got it. Medaled.
 one year ago

theEricBest ResponseYou've already chosen the best response.1
Cool! Would you just have to memorize \[\frac{7\pi}{6}\] and \[\frac{11\pi}{6}\]? I think you would have to...
 one year ago

theEricBest ResponseYou've already chosen the best response.1
Ah well, I'll recap another day! I'm glad I could be of some service! Take care!
 one year ago

MathCuriousBest ResponseYou've already chosen the best response.1
I wouldn't really memorize, but it's not a bad idea if you have that capacity! :) If anything it would be convenient. However, there is a method to finding it with logic. If the Ycoordinate is 1/2 then the x must be \[\sqrt{3}\div2\] this is assuming we understand the basic triangles. This information tells us with an xcoord of 1/2 and a ycoord of \[\sqrt{3}\div2\] it is a 30 degree angle (in quadrant I). However the problem needs a solution for where Y is negative. dw:1350355894146:dw It is true in two quadrants. The formula for DEGREES to RADIANS is:( DEGREE*PI )/ 180 since quadrant III begins from 180 and ends at 270 AND we knew it is essentially a 30 degree angle then we can add 30 DEGREES to 180. This becomes a 210 angle. Divide 270 by 180 and you get 7/6. Don't forget to multiply it by Pi. Hopefully that shows how to get an angle in another quadrant. There are of course other tricks to get there. dw:1350356151031:dw You could see this visually. You could just directly reflect the angle into an opposite quadrant by making a straight line out of it. Here it has 180 degrees added to it. So you don't need to just simply memorize radians.
 one year ago
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