Inverse Trig Functions

Front

What is the range of the inverse sine function, sin^-1(x)?

Back

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

Front

What is the range of the inverse cosine function, cos^-1(x)?

Back

The range of cos^-1(x) is [0, π].

Front

What is the range of the inverse tangent function, tan^-1(x)?

Back

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

Front

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

Back

If y = sin^-1(x), then sin(y) = x for x in [-1, 1].

Front

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

Back

If y = cos^-1(x), then cos(y) = x for x in [-1, 1].

Front

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

Back

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

Front

Evaluate: sin^-1(1).

Back

sin^-1(1) = π/2.

Front

Evaluate: cos^-1(1).

Back

cos^-1(1) = 0.

Front

Evaluate: tan^-1(0).

Back

tan^-1(0) = 0.

Front

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

Back

sin(cos^-1(x)) = √(1 - x²) for x in [0, 1].