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
Graphical? or Algebraic?
Graph: https://www.desmos.com/calculator/g6jxv3grvh
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
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