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


cos s = 0.7826

Key Concepts

Cosine Function

The cosine function, denoted as cos, is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is defined for all real numbers and is periodic with a period of 2π. In the context of the unit circle, cos(s) represents the x-coordinate of a point on the circle corresponding to the angle s.

Inverse Cosine (arccos)

The inverse cosine function, or arccos, is used to find the angle whose cosine is a given value. It is defined for values in the range [-1, 1] and returns angles in the interval [0, π]. This function is essential for solving equations involving cosine, such as finding the angle s when cos(s) = 0.7826.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. In this case, the interval [0, π/2] indicates that s must be between 0 and π/2, inclusive. Understanding this notation is crucial for determining the valid solutions for s, as it restricts the possible angles to the first quadrant where cosine values are positive.