Inverse Trig Functions

Front

What is the definition of inverse trigonometric functions?

Back

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

Front

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

Back

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

Front

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

Back

The range of cos^-1(x) is [0, π].

Front

What is the range of the 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, where -1 ≤ x ≤ 1.

Front

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

Back

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

Front

Calculate csc^-1(-√(2)).

Back

csc^-1(-√(2)) = -π/4.

Front

Calculate tan(sin^-1(-1/2)).

Back

tan(sin^-1(-1/2)) = -√3/3.

Front

Calculate tan^-1(-√3).

Back

tan^-1(-√3) = -π/3.