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 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 for finding the angle using the sine function?

Back

x = sin⁻¹(opposite/hypotenuse) or x = arcsin(opposite/hypotenuse).

Front

What is the formula for finding the angle using the cosine function?

Back

x = cos⁻¹(adjacent/hypotenuse) or x = arccos(adjacent/hypotenuse).

Front

What is the formula for finding the angle using the tangent function?

Back

x = tan⁻¹(opposite/adjacent) or x = arctan(opposite/adjacent).

Front

If sin(x) = 3/5, what is x?

Back

x = sin⁻¹(3/5).

Front

If cos(x) = 4/5, what is x?

Back

x = cos⁻¹(4/5).

Front

If tan(x) = 1, what is x?

Back

x = tan⁻¹(1) = 45° or π/4 radians.

Front

What is the range of the arcsin function?

Back

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

Front

What is the range of the arccos function?

Back

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