Solve Trig Question: 14sin^2y-13=0 for y where 0<y<360

  • Thread starter Thread starter Checkfate
  • Start date Start date
  • Tags Tags
    Trig
AI Thread Summary
To solve the equation 14sin²y - 13 = 0 for y in the range 0 < y < 360, the correct approach involves factoring and using the arcsine function. The initial solutions found are y = 74.5° and y = 285.5°, but additional solutions are needed. The missing angles, 105.5° and 254.5°, are derived from the properties of the sine function, specifically using the identity sin(180° - θ) and the periodic nature of sine. The final solutions for y are 74.5°, 105.5°, 254.5°, and 285.5°. This highlights the importance of considering all possible angles within the specified range.
Checkfate
Messages
149
Reaction score
0
Hello,

I am running into an error and I can't quite figure out what I am doing wrong.

The question is "solve 14\sin^{2}y-13=0 for y where 0<y<360.

So I factor it down to

14(sin(y)-\frac{\sqrt{182}}{14})(sin(y)+\frac{\sqrt{182}}{14})=0 (Thanks integral for showing me how to do this) :P

and thus get

y=74.5\deg or y=285.5\deg by using arcsine, but I am missing solutions somehow. I checked my answer with my calc and it's wrong, I am missing 105.5^ and 254.5^... how though? Adding the period length of 360^ does absolutely nothing. It's probably a small detail that I am overlooking, can someone point me in the right direction? Thanks again.
 
Physics news on Phys.org
180 - 74.5 = 105.5

360 - 105.5 = 254.5
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
Back
Top