Rewrite the following expression as an algebraic expression in x:
cos(arcsin(x))
make a sketch of a rightangled triangle
label the base angle Ø, then opposite side is x
hypotenuse is 1
then the adjacent side is √(1 - x^2)
so cos(arcsin(x)) = √(1-x^2)1
To rewrite the expression "cos(arcsin(x))" as an algebraic expression in x, we need to understand the properties of inverse trigonometric functions.
The inverse trigonometric function arcsin(x) represents the angle whose sine is x. So, cos(arcsin(x)) represents the cosine of the angle whose sine is x.
To find the value of cos(arcsin(x)), we can use the identity:
cos(arcsin(x)) = √(1 - sin^2(arcsin(x)))
Since sin(arcsin(x)) = x, we can substitute this value into the expression:
cos(arcsin(x)) = √(1 - x^2)
Therefore, the algebraic expression for cos(arcsin(x)) is √(1 - x^2).