Could you me with this question?

[phy_]

-10.5 = 3.8 cos [2pi/360(x-172)] this is the question and i am trying to solve for x though i don't know that i can break away the x from cos the way i did... is there another way??
i don't think the answer should be negative as the question is looking for a day of the year.

so if i try to solve for x, i end up with

-2.76 = cos [0.017x - 2.924]

-1.8876 = cos 0.017x

-1.8876/0.9999 = x

x = -1.8878

 

[Mentallic]

There is no solution to the equation.

Reason is that the cosine of a value ranges between -1 and 1.

$$A=Bcos\theta$$

$$cos\theta=\frac{A}{B}$$

Therefore, to have a real solution for $\theta$, $$-1\leq \frac{A}{B}\leq 1$$

But in the case of your equation:

$$-10.5=3.8cos(\frac{2\pi (x-172)}{360})$$

$$cos(\frac{2\pi (x-172)}{360})=\frac{-10.5}{3.8}$$