Question

Solve for the solutions of the equation cos(x) = √3/2.

A) x = π/6 + 2πn, x = 11π/6 + 2πn
B) x = π/3 + 2πn, x = 5π/3 + 2πn
C) x = π/4 + 2πn, x = 7π/4 + 2πn
D) x = π/2 + 2πn, x = 3π/2 + 2πn

Answer 1

The solutions for cos(x) = √3/2 are x = π/6 + 2πn and x = 11π/6 + 2πn, which represent angles in the first and fourth quadrants, factoring in the periodic nature of the cosine function.

Step-by-step explanation:

The equation to solve for the solutions of the equation cos(x) = √3/2 asks us to find all the angles x for which the cosine function has the value of √3/2. Recall that cosine values are positive in the first and fourth quadrants, which corresponds to angles of π/6 and 11π/6, respectively. Since trigonometric functions are periodic, we need to include all co-terminal angles by adding multiples of 2π.

Therefore, the solutions to the equation cos(x) = √3/2 are given by:

1. x = π/6 + 2πn, where n is an integer (for the first quadrant)
2. x = 11π/6 + 2πn, where n is an integer (for the fourth quadrant)

So, the correct answer is: A) x = π/6 + 2πn, x = 11π/6 + 2πn.