evaluate and graph inverse trigonometric functions

Front

Define inverse trigonometric functions.

Back

Inverse trigonometric functions are functions that reverse the action of the standard trigonometric functions. They take a ratio (like sine, cosine, or tangent) and return an angle. The main inverse functions are sin^-1, cos^-1, and tan^-1.

Front

What is the range of sin^-1(x)?

Back

The range of sin^-1(x) is [-π/2, π/2].

Front

What is the range of cos^-1(x)?

Back

The range of cos^-1(x) is [0, π].

Front

What is the range of tan^-1(x)?

Back

The range of tan^-1(x) is (-π/2, π/2).

Front

Evaluate sin^-1(0).

Back

sin^-1(0) = 0.

Front

Evaluate cos^-1(1).

Back

cos^-1(1) = 0.

Front

Evaluate tan^-1(0).

Back

tan^-1(0) = 0.

Front

What is the relationship between sin^-1(x) and sin(y)?

Back

If y = sin^-1(x), then sin(y) = x.

Front

What is the relationship between cos^-1(x) and cos(y)?

Back

If y = cos^-1(x), then cos(y) = x.

Front

What is the relationship between tan^-1(x) and tan(y)?

Back

If y = tan^-1(x), then tan(y) = x.