Chapter 7.7 Inverse Functions 2024

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, swap the x and y in the equation and solve for y.

Front

What is the relationship between a function and its inverse?

Back

The graph of a function and its inverse are reflections of each other across the line y = x.

Front

What is the sine function?

Back

The sine function, sin(θ), is a trigonometric function that represents the ratio of the length of the opposite side to the hypotenuse in a right triangle.

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1].

Front

What is the purpose of the inverse sine function (sin⁻¹)?

Back

The inverse sine function is used to find the angle whose sine is a given value.

Front

How do you calculate sin⁻¹(x)?

Back

To calculate sin⁻¹(x), use a calculator or trigonometric tables to find the angle whose sine is x.

Front

What is the sine rule in trigonometry?

Back

The sine rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C).

Front

What is the cosine function?

Back

The cosine function, cos(θ), is a trigonometric function that represents the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Front

What is the range of the cosine function?

Back

The range of the cosine function is also [-1, 1].