12/17 review inverse Trigonometric Functions

Front

What is the definition of inverse trigonometric functions?

Back

Inverse trigonometric functions are functions that return the angle whose trigonometric function value is a given number. They include arcsin, arccos, and arctan.

Front

What is the range of the function arccos(x)?

Back

The range of arccos(x) is [0, π].

Front

What is the value of arccos(cos(θ)) for θ in the range [0, 2π]?

Back

arccos(cos(θ)) = θ if 0 ≤ θ ≤ π; otherwise, arccos(cos(θ)) = 2π - θ.

Front

What is the value of tan(arccos(x))?

Back

Front

What is the principal value of tan^{-1}(-1)?

Back

Front

Back

Front

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

Back

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

Front

What is the relationship between sin and arcsin?

Back

If y = sin(x), then x = arcsin(y), where x is in the range [-π/2, π/2].

Front

What is the value of tan(cos^{-1}(-1))?

Back

The value of tan(cos^{-1}(-1)) is 0.

Front

What is the domain of the function arctan(x)?

Back

The domain of arctan(x) is all real numbers (-∞, ∞).