SOLUTION: The equation 4sin[n(xdegrees-h)]+3=5 has solutions of 125degrees and 545degrees. What are the values of n and h? I solved and got h=20 snf n=2/7 but im not sure if there are mor

Algebra ->  Trigonometry-basics -> SOLUTION: The equation 4sin[n(xdegrees-h)]+3=5 has solutions of 125degrees and 545degrees. What are the values of n and h? I solved and got h=20 snf n=2/7 but im not sure if there are mor      Log On


   

Question 1129292: The equation 4sin[n(xdegrees-h)]+3=5 has solutions of 125degrees and 545degrees. What are the values of n and h?
I solved and got h=20 snf n=2/7 but im not sure if there are more answers.
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Your answer is good.

4sin%28%282%2F7%29%28x-20%29%29%2B3+=+5

But yes, there ARE more answers.

The equation simplifies to

sin%28n%28x-h%29%29+=+.5

The value of sine is 0.5 at 30 degrees and 150 degrees.

So if the two given solutions of 125 and 545 degrees are the two smallest positive solutions where the value of sine is 1/2, then your answers are correct, because the two values of x should correspond to 30 and 150 degrees. And in your solution, they do:

(2/7)(125-20) = (2/7)(105) = 30
(2/7)(545-20) = (2/7)(525) = 150

But the solutions 125 and 545 degrees might be (for example) the 2nd and 5th positive solutions, corresponding to angles of 150 and 750 degrees. Then it turns out that n=10/7 while h is again 20:

(10/7)(125-20) = 150
(10/7)(545-20) = 750

Then the equation is

4sin%28%2810%2F7%29%28x-20%29%29%2B3+=+5

Here is a graph showing the two functions (yours red; mine green) and the line y=5:



The graph clearly shows your function having the value 5 at the 1st and 2nd positive values of x while mine has the value 5 at the 2nd and 5th positive values of x.

And of course you can get an infinite number of similar solutions, by choosing any two angles for which the value of sine is 0.5 to be the ones corresponding to the given solutions of 125 and 545 degrees.