The general solution of cos θ = 0 is

• θ = nπ
• θ = (2n + 1)π/2
• θ = 2nπ
• θ = (2n - 1)π/2

The equation cos θ = 0 has specific solutions based on the properties of the cosine function. To find the general solution, we need to identify the angles where the cosine value equals zero.

Key Solutions

The cosine function equals zero at odd multiples of π/2. Therefore, the general solution can be expressed as:

• θ = (2n + 1)π/2, where n is any integer.

Explanation of the Solution

This formula indicates that for every integer value of n, you can find an angle θ where the cosine is zero. For example:

• If n = 0, then θ = π/2.
• If n = 1, then θ = 3π/2.
• If n = -1, then θ = -π/2.

Other options like θ = nπ or θ = 2nπ do not yield solutions for cos θ = 0, as they correspond to angles where the cosine value is either 1 or -1, not zero.

Summary

In summary, the correct general solution for cos θ = 0 is:

• θ = (2n + 1)π/2

This captures all angles where the cosine function equals zero.