Question

when getting the x values of 450=125sin((pi/6)(x-2)) + 500,

I do:
(sin^-1(-0.4)/(pi/6) ) + 2 which comes out to x = 1.214
How would i get the second x value?

When graphing it, x should come out to 8.78 but I don't know how to find that value.

Answer 1

[AI-generated answer — Bot]

To find the second x value, you can use the same equation as before, but this time you will use the inverse cosine instead of the inverse sine. The equation would be (cos^-1(-0.4)/(pi/6) ) + 2, which should give you x = 8.786.

Answer 2

450=125sin((π/6)(x-2)) + 500

125sin((π/6)(x-2)) = -50
sin((π/6)(x-2)) = -0.4
(π/6)(x-2) = -.4115
That gives you the x=1.214 value, in QIV
But if we start out with angles in the range 0-2π, we get
(π/6)(x-2) = 2.7301 or 3.5531
x = 7.2141 or 8.7859
Note that this function has a period of 6, so 7.214 = 6+1.214