Find angles using Trig (Inverses!)

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 purpose of using inverse trigonometric functions?

Back

They are used to find angles when the lengths of the sides of a triangle are known.

Front

How do you find the angle using the sine function?

Back

To find the angle, use the formula: angle = arcsin(opposite/hypotenuse).

Front

How do you find the angle using the cosine function?

Back

To find the angle, use the formula: angle = arccos(adjacent/hypotenuse).

Front

How do you find the angle using the tangent function?

Back

To find the angle, use the formula: angle = arctan(opposite/adjacent).

Front

What is the range of the arcsin function?

Back

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

Front

What is the range of the arccos function?

Back

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

Front

What is the range of the arctan function?

Back

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

Front

If sin(θ) = 0.5, what is θ?

Back

θ = 30° or θ = 150° (in the range of 0° to 360°).

Front

If cos(θ) = 0.6, what is θ?

Back

θ = 53.1° or θ = 306.9° (in the range of 0° to 360°).