25.3-25.4 (Composition of Inverse Trig Functions)

Front

What is the composition of inverse tangent and tangent?

Back

For any real number x, tan(arctan(x)) = x.

Front

What is the composition of inverse cosine and cosine?

Back

For angles in the range [0, π], arccos(cos(x)) = x.

Front

What is the range of the inverse sine function?

Back

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

Front

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

Back

tan(sin^-1(1)) = 1.

Front

What is the value of tan(sin^-1(-1/2))?

Back

tan(sin^-1(-1/2)) = -√(3)/3.

Front

What is the value of tan[arctan(10)]?

Back

tan[arctan(10)] = 10.

Front

What is the value of arccos[cos(2π/3)]?

Back

arccos[cos(2π/3)] = 2π/3.

Front

What is the domain of the inverse sine function?

Back

The domain of sin^-1(x) is [-1, 1].

Front

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

Back

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

Front

What is the value of sin(arcsin(1/2))?

Back

sin(arcsin(1/2)) = 1/2.