Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.4924

Key Concepts

Sine Function

The sine function, denoted as sin, is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse. It is periodic and oscillates between -1 and 1. In the context of the unit circle, sin(s) represents the y-coordinate of a point on the circle corresponding to the angle s.

Inverse Sine Function

The inverse sine function, or arcsin, is used to determine the angle whose sine is a given value. It is denoted as sin⁻¹ or arcsin and is defined for values in the range [-1, 1]. The output of arcsin is restricted to the interval [-π/2, π/2], but when considering the sine function's periodicity, we can find multiple angles that yield the same sine value.

Interval [0, π/2]

The interval [0, π/2] represents the first quadrant of the unit circle, where both sine and cosine functions are positive. In this interval, the sine function is increasing, meaning that as the angle s increases from 0 to π/2, the value of sin(s) also increases from 0 to 1. This property is crucial for finding the angle s that satisfies the equation sin(s) = 0.4924 within the specified range.