Trig Inverses

Front

What is the definition of arccos(x)?

Back

Arccos(x) is the inverse function of the cosine function, which returns the angle whose cosine is x, typically in the range [0, π].

Tags

CCSS.HSF.BF.B.5

Front

What is the value of arccos(0)?

Back

The value of arccos(0) is π/2.

Tags

CCSS.HSF.TF.B.7

Front

What is the value of arccos(-√3/2)?

Back

The value of arccos(-√3/2) is 5π/6.

Tags

CCSS.HSF.TF.B.7

Front

What is the definition of arcsin(x)?

Back

Arcsin(x) is the inverse function of the sine function, which returns the angle whose sine is x, typically in the range [-π/2, π/2].

Tags

CCSS.HSF-BF.B.4D

Front

What is the value of sin^-1(sin π/4)?

Back

The value of sin^-1(sin π/4) is π/4.

Tags

CCSS.HSF.TF.B.7

Front

What is the range of angles for the inverse sine function?

Back

The range of angles for the inverse sine function is from -π/2 to π/2.

Tags

CCSS.HSF-BF.B.4D

Front

What is the definition of arctan(x)?

Back

Arctan(x) is the inverse function of the tangent function, which returns the angle whose tangent is x, typically in the range (-π/2, π/2).

Tags

CCSS.HSF-BF.B.4A

Front

What is the value of arctan(1)?

Back

The value of arctan(1) is π/4.

Front

What is the relationship between sine and cosine in terms of their inverses?

Back

The sine and cosine functions are co-functions; specifically, sin(θ) = cos(π/2 - θ) and cos(θ) = sin(π/2 - θ).

Tags

CCSS.HSF.TF.A.4

Front

What is the principal value of an inverse trigonometric function?

Back

The principal value is the unique output of an inverse trigonometric function that lies within its defined range.

Tags

CCSS.HSF.TF.B.7