M II 4.2.3 Inverse Trig Functions - Equations only

Front

What is the definition of the inverse sine function (sin^–1)?

Back

The inverse sine function, denoted as sin^–1(x) or arcsin(x), is the function that returns the angle whose sine is x, where x is in the range [-1, 1].

Front

What is the definition of the inverse cosine function (cos^–1)?

Back

The inverse cosine function, denoted as cos^–1(x) or arccos(x), is the function that returns the angle whose cosine is x, where x is in the range [-1, 1].

Front

What is the definition of the inverse tangent function (tan^–1)?

Back

The inverse tangent function, denoted as tan^–1(x) or arctan(x), is the function that returns the angle whose tangent is x, for all real numbers x.

Front

How do you solve for an angle using the inverse sine function?

Back

To solve for an angle using the inverse sine function, you use the equation x = sin^–1(opposite/hypotenuse), where 'opposite' is the length of the side opposite the angle and 'hypotenuse' is the length of the hypotenuse.

Front

How do you solve for an angle using the inverse cosine function?

Back

To solve for an angle using the inverse cosine function, you use the equation x = cos^–1(adjacent/hypotenuse), where 'adjacent' is the length of the side adjacent to the angle and 'hypotenuse' is the length of the hypotenuse.

Front

How do you solve for an angle using the inverse tangent function?

Back

To solve for an angle using the inverse tangent function, you use the equation x = tan^–1(opposite/adjacent), where 'opposite' is the length of the side opposite the angle and 'adjacent' is the length of the side adjacent to the angle.

Front

What is the range of the inverse sine function?

Back

The range of the inverse sine function (sin^–1) is [-π/2, π/2] or [-90°, 90°].

Front

What is the range of the inverse cosine function?

Back

The range of the inverse cosine function (cos^–1) is [0, π] or [0°, 180°].

Front

What is the range of the inverse tangent function?

Back

The range of the inverse tangent function (tan^–1) is (-π/2, π/2) or (-90°, 90°).

Front

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

Back

For complementary angles, sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ).