Inverse Trig Ratios

Front

What is the definition of inverse trigonometric functions?

Back

Inverse trigonometric functions are functions that determine the angle whose trigonometric ratio is a given number. They include arcsin, arccos, and arctan.

Front

What is the range of the arcsin function?

Back

The range of the arcsin function is [-π/2, π/2] or [-90º, 90º].

Front

What is the range of the arccos function?

Back

The range of the arccos function is [0, π] or [0º, 180º].

Front

What is the range of the arctan function?

Back

The range of the arctan function is (-π/2, π/2) or (-90º, 90º).

Front

How do you express sin(x) = 11/27 in terms of x?

Back

x = arcsin(11/27).

Front

How do you express cos(x) = 6/8 in terms of x?

Back

x = arccos(6/8) or x = arccos(0.75).

Front

What is the relationship between sine and cosine in a right triangle?

Back

In a right triangle, sine is the ratio of the length of the opposite side to the hypotenuse, while cosine is the ratio of the length of the adjacent side to the hypotenuse.

Front

What is the formula to find the angle using cosine?

Back

The formula to find the angle using cosine is x = cos^(-1)(adjacent/hypotenuse).

Front

What is the formula to find the angle using sine?

Back

The formula to find the angle using sine is x = sin^(-1)(opposite/hypotenuse).

Front

What is the formula to find the angle using tangent?

Back

The formula to find the angle using tangent is x = tan^(-1)(opposite/adjacent).