Solve each equation for x, where x is restricted to the given interval.
y = 5 cos x , for x in [0, π]

Key Concepts

Cosine Function

The cosine function, denoted as cos(x), is a fundamental trigonometric function that relates the angle x to the ratio of the adjacent side to the hypotenuse in a right triangle. It oscillates between -1 and 1, with a period of 2π. Understanding its behavior is crucial for solving equations involving cosine, especially within specified intervals.

Solving Trigonometric Equations

Solving trigonometric equations involves finding the values of the variable (in this case, x) that satisfy the equation. This often requires using inverse trigonometric functions, identities, and understanding the periodic nature of trigonometric functions. The solution must also respect any given restrictions on the variable, such as the interval [0, π].

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. In this context, [0, π] indicates that x can take any value from 0 to π, inclusive. Understanding interval notation is essential for determining valid solutions to the equation, as it restricts the possible values of x to a specific range.