Review Math 3

Front

What are inverse functions?

Back

Inverse functions are functions that reverse the effect of the original function. If f(x) is a function, then its inverse f^(-1)(x) satisfies the equation f(f^(-1)(x)) = x.

Front

How do you determine if two functions are inverses?

Back

To determine if two functions are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain of f and g.

Front

What is the general equation for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Front

If the volume of a cylinder is 150 in³ and the radius is 4 in, how do you find the height?

Back

Use the formula V = πr²h. Rearranging gives h = V / (πr²). Plugging in the values gives h = 150 / (π * 4²) ≈ 3 in.

Front

What is the amplitude of the function y = 2 sin x?

Back

The amplitude of a sine function y = A sin(Bx) is |A|. For y = 2 sin x, the amplitude is 2.

Front

What is the period of the function y = sin x?

Back

The period of the sine function y = sin x is 2π.

Front

What is the difference between sine and cosine functions?

Back

Sine and cosine are both periodic functions. Sine represents the y-coordinate of a point on the unit circle, while cosine represents the x-coordinate.

Front

How do you find the arc length of a circle?

Back

The arc length L of a circle is given by the formula L = rθ, where r is the radius and θ is the angle in radians.

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².