draw a right angled triangle.
mark one of the acute angles $$\theta$$
$$\theta$$ = asin (x/1)
now
$$sin\theta = \frac{opp}{hyp}=\frac{1}{x}$$
put 1 on the opp side and x on the hypotenuse
find the adjacent side using the pythagorean theorem.
so you can read cos $$\theta$$ off the triangle.
BUT
You should consider the possible quadrants
if x is positive $$\theta$$ will be in the first quad so cos$$\theta$$ is also positive.
if x is negative $$\theta$$ will be in the 4ht quad so cos$$\theta$$ will be positive also.
draw a right angled triangle.
mark one of the acute angles $$\theta$$
$$\theta$$ = asin (x/1)
now
$$sin\theta = \frac{opp}{hyp}=\frac{1}{x}$$
put 1 on the opp side and x on the hypotenuse
find the adjacent side using the pythagorean theorem.
so you can read cos $$\theta$$ off the triangle.
BUT
You should consider the possible quadrants
if x is positive $$\theta$$ will be in the first quad so cos$$\theta$$ is also positive.
if x is negative $$\theta$$ will be in the 4ht quad so cos$$\theta$$ will be positive also.