Mastering Inverse Sine: The Function And Its Properties In Trigonometry.

Inverse Sin

1/√(1-x^2)

Inverse sine, also known as arcsine, is an inverse trigonometric function that finds the angle whose sine equals a given value. In other words, it takes a value between -1 and 1 and returns an angle.

The notation for inverse sine is sin⁻¹ or arcsin. For example, sin⁻¹(0.5) or arcsin(0.5) returns the angle whose sine is 0.5.

To find the inverse sine of a value, we can use a scientific calculator or a table of values. However, we must be careful when using inverse sine because it has restrictions. Sine is a periodic function, and we can get multiple angles with the same sine value. Therefore, the inverse sine function returns the principal value, which is the angle between -π/2 and π/2 radians or between -90° and 90°.

Here are some properties of inverse sine:

1. Domain: The domain of inverse sine is [-1, 1].
2. Range: The range of inverse sine is [-π/2, π/2] or [-90°, 90°] in degrees.
3. Symmetry: Inverse sine is an odd function, which means sin⁻¹(-x) = -sin⁻¹(x).
4. Derivative: The derivative of inverse sine is 1/√(1-x²).
5. Identity: sin(sin⁻¹(x)) = x.

Overall, inverse sine is a useful tool in trigonometry when working with angles and sine values.

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