Inverse Trig Functions

Front

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

Back

The range of cos^-1(x) is [0, π].

Tags

CCSS.HSF-BF.B.4D

Front

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

Back

The inverse sine function, sin^-1(x), gives the angle whose sine is x, with a range of [-π/2, π/2].

Tags

CCSS.HSF-BF.B.4D

Front

What is the relationship between the sine and cosine of complementary angles?

Back

For any angle θ, sin(θ) = cos(π/2 - θ).

Tags

CCSS.HSF.TF.C.8

Front

How do you find the value of tan(sin^-1(x))?

Back

To find tan(sin^-1(x)), use the identity tan(θ) = sin(θ)/cos(θ) where θ = sin^-1(x).

Tags

CCSS.HSF.TF.C.8

Front

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

Back

The domain of tan^-1(x) is all real numbers, (-∞, ∞).

Front

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

Back

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

Tags

CCSS.HSF.TF.B.7

Front

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

Back

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

Tags

CCSS.HSF.TF.B.7

Front

What is the relationship between the cosecant and sine functions?

Back

Csc(θ) = 1/sin(θ), where θ is the angle.

Tags

CCSS.HSF.TF.A.2

Front

What is the value of sec^-1(x) when x = 2?

Back

The value of sec^-1(2) is π/3.

Tags

CCSS.HSF.TF.B.7

Front

What is the value of csc(cos^-1(x))?

Back

csc(cos^-1(x)) = 1/sqrt(1-x²) for x in the range [0, 1].

Tags

CCSS.HSF.TF.C.8