Lt 5.4 Inverse Trig 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 and return an angle. The main inverse trigonometric functions are sin^-1, cos^-1, and tan^-1.

Front

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

Back

The range of the inverse sine function, 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 the inverse cosine function, cos^-1(x), is [0, π].

Front

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

Back

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

Front

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

Back

The relationship is given by: sin^-1(x) + cos^-1(x) = π/2 for x in [0, 1].

Front

Evaluate sin^-1(cos(5π/6)).

Back

sin^-1(cos(5π/6)) = -π/3.

Front

Evaluate tan(cos^-1(-1)).

Back

tan(cos^-1(-1)) = 0.

Front

What is the value of arctan[tan(2π/3)]?

Back

arctan[tan(2π/3)] = -π/3.

Front

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

Back

The domain of the inverse sine function, sin^-1(x), is [-1, 1].

Front

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

Back

The domain of the inverse cosine function, cos^-1(x), is [-1, 1].