the sine function is a many-to-one function and therefore has no inverse function.
However if the domain is restricted to -90° ≤ x ≤ 90°
Then the function is one-to-one for this domain
Thus, x is defined as the angle such that - π/2 ≤ x ≤ π/2
5π/6 is therefore outwith the domain
Answer:
The volume of the cone is approximately 453.0 cm³
Step-by-step explanation:
The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.
However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:
So we can find the height of the cone with that:
Now that we have the cone's height, we can solve for its volume:
