why are some trigonometric substitutions not explained in books? In some books I find trigonometric substitution explained for only 3 cases
in which one is: 
$$\sqrt{a^2-x^2}=acos\theta$$
but so far i've never seen this one
$$\sqrt{a^2-x^2}=asin\theta$$
I believe it's a legit substitution since  you can choice where to put the angle in the triangle. Why does nobody explain this one?

Imagine a triangle whose vertices are (-a,0), (a,0) and (0,a), the first substitution is an intersection of between the sides of this triangle with horizontal lines from -a to a, the second substitution is an intersection if the sides of the triangle with vertical lines from 0 to a.
