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-4=4sin(360/70(x-12.5))-2 whats the answer ?

 Dec 16, 2015

Best Answer 

 #3
avatar+129907 
+5

It's a little unclear as to what you have, but.....I'll give it a shot :

 

-4=4sin([360/70](x-12.5))-2      add 2 to both sides

 

-2  = 4 sin [(36/7)x - 450/7]     divide both sides by 4

 

-1/2  = sin [(36/7)x  - 450/7]

 

The sin  =  -1/2 at  210°  and at 330°

 

So  solving

 

(36/7)x - 450/7  = 210

 

36x - 450   =  1470

 

36x = 1920

 

x = [160/3]°   ≈ 53.333°......     with the 3s repeating

 

And solving

 

(36/7)x - 450/7  = 330

 

36x - 450 = 2310

 

36x  = 2760

 

x = [230/3]° ≈  76.666°.......  with the 6s repeating

 

The more general solutions......as shown by this graph......   https://www.desmos.com/calculator/gh9a73uifc .....    are

 

x = [160/3]°  + n*70°     where n is an integer      and

 

x = [230/3]° + n*70°   where n is an integer

 

 

 

cool cool cool

 Dec 16, 2015
 #1
avatar+2592 
0

Graphical? or Algebraic?

 

Graph: https://www.desmos.com/calculator/g6jxv3grvh

 Dec 16, 2015
 #2
avatar
+5

Solve for x:
-4 = 4 sin((36 (x-12.5))/7)-2

4 sin((36 (x-12.5))/7)-2 = 4 sin(36/7 (x-25/2))-2:
-4 = 4 sin(36/7 (x-25/2))-2

-4 = 4 sin(36/7 (x-25/2))-2 is equivalent to 4 sin(36/7 (x-25/2))-2 = -4:
4 sin(36/7 (x-25/2))-2 = -4

Add 2 to both sides:
4 sin(36/7 (x-25/2)) = -2

Divide both sides by 4:
sin(36/7 (x-25/2)) = -1/2

Take the inverse sine of both sides:
36/7 (x-25/2) = (7 pi)/6+2 pi n_1  for  n_1  element Z
   or  36/7 (x-25/2) = (11 pi)/6+2 pi n_2  for  n_2  element Z

Multiply both sides by 7/36:
x-25/2 = (49 pi)/216+(7 pi n_1)/18  for  n_1  element Z
   or  36/7 (x-25/2) = (11 pi)/6+2 pi n_2  for  n_2  element Z

Add 25/2 to both sides:
x = 25/2+(49 pi)/216+(7 pi n_1)/18  for  n_1  element Z
   or  36/7 (x-25/2) = (11 pi)/6+2 pi n_2  for  n_2  element Z

Multiply both sides by 7/36:
x = 25/2+(49 pi)/216+(7 pi n_1)/18  for  n_1  element Z
   or  x-25/2 = (77 pi)/216+(7 pi n_2)/18  for  n_2  element Z

Add 25/2 to both sides:
Answer: | x = 1.22173 n+12.3982 and n element Z  and x = x = 1.22173 n+13.2127 and n element Z

 Dec 16, 2015
 #3
avatar+129907 
+5
Best Answer

It's a little unclear as to what you have, but.....I'll give it a shot :

 

-4=4sin([360/70](x-12.5))-2      add 2 to both sides

 

-2  = 4 sin [(36/7)x - 450/7]     divide both sides by 4

 

-1/2  = sin [(36/7)x  - 450/7]

 

The sin  =  -1/2 at  210°  and at 330°

 

So  solving

 

(36/7)x - 450/7  = 210

 

36x - 450   =  1470

 

36x = 1920

 

x = [160/3]°   ≈ 53.333°......     with the 3s repeating

 

And solving

 

(36/7)x - 450/7  = 330

 

36x - 450 = 2310

 

36x  = 2760

 

x = [230/3]° ≈  76.666°.......  with the 6s repeating

 

The more general solutions......as shown by this graph......   https://www.desmos.com/calculator/gh9a73uifc .....    are

 

x = [160/3]°  + n*70°     where n is an integer      and

 

x = [230/3]° + n*70°   where n is an integer

 

 

 

cool cool cool

CPhill Dec 16, 2015

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