Inverse Trigonometric Ratios (arcsine, arccosine, arctangent

Front

What is the definition of arcsine?

Back

Arcsine (sin⁻¹) is the inverse function of the sine function, used to find the angle whose sine is a given number.

Front

What is the definition of arccosine?

Back

Arccosine (cos⁻¹) is the inverse function of the cosine function, used to find the angle whose cosine is a given number.

Front

What is the definition of arctangent?

Back

Arctangent (tan⁻¹) is the inverse function of the tangent function, used to find the angle whose tangent is a given number.

Front

What is the range of the arcsine function?

Back

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

Front

What is the range of the arccosine function?

Back

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

Front

What is the range of the arctangent function?

Back

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

Front

If sin(θ) = 0.5, what is θ using arcsine?

Back

θ = arcsin(0.5) = 30°.

Front

If cos(θ) = 0.5, what is θ using arccosine?

Back

θ = arccos(0.5) = 60°.

Front

If tan(θ) = 1, what is θ using arctangent?

Back

θ = arctan(1) = 45°.

Front

What is the relationship between sine and arcsine?

Back

If y = sin(θ), then θ = arcsin(y).