Inverse Trig Functions

Front

What is the definition of the cosecant function (csc)?

Back

The cosecant function is the reciprocal of the sine function, defined as csc(x) = 1/sin(x).

Front

What is the relationship between inverse trigonometric functions and their corresponding trigonometric functions?

Back

Inverse trigonometric functions return the angle whose trigonometric function value is given. For example, if y = sin(x), then x = sin^-1(y).

Front

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

Back

The range of the inverse sine function is [-π/2, π/2].

Front

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

Back

The range of the inverse cosine function is [0, π].

Front

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

Back

The range of the inverse tangent function is (-π/2, π/2).

Front

How do you calculate csc(cos^-1(x))?

Back

To calculate csc(cos^-1(x)), first find the angle θ such that cos(θ) = x, then use the identity csc(θ) = 1/sin(θ).

Front

What is the value of sin(cos^-1(0))?

Back

The value of sin(cos^-1(0)) is 1.

Front

What is the value of cos^-1(tan(-π/4))?

Back

The value of cos^-1(tan(-π/4)) is π.

Front

What is the domain of the inverse sine function (sin^-1)?

Back

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

Front

What is the domain of the inverse cosine function (cos^-1)?

Back

The domain of the inverse cosine function is [-1, 1].