What are the solutions of the equation sin(x) = sin(π/3)?

₹0.0

Question: What are the solutions of the equation sin(x) = sin(π/3)?

Options:

Correct Answer: x = π/3

Solution:

The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.

What are the solutions of the equation sin(x) = sin(π/3)?

What are the solutions of the equation sin(x) = sin(π/3)?

Step 1: Understand the equation sin(x) = sin(π/3). This means we are looking for values of x where the sine of x is equal to the sine of π/3.
Step 2: Recall that sin(π/3) is a specific value. It equals √3/2.
Step 3: The sine function is periodic, meaning it repeats its values. The sine function equals a specific value at multiple angles.
Step 4: The first angle where sin(x) = sin(π/3) is x = π/3.
Step 5: The sine function is also equal to sin(π/3) at another angle in the range of 0 to 2π, which is x = 2π/3.
Step 6: Since the sine function repeats every 2π, we can add multiples of 2π to both solutions. This gives us the general solutions: x = π/3 + 2nπ and x = 2π/3 + 2nπ, where n is any integer.

Trigonometric Equations – The question tests the understanding of solving trigonometric equations, specifically using the properties of the sine function.
Periodic Functions – It assesses knowledge of the periodic nature of the sine function and how to express general solutions.
Reference Angles – The question involves identifying reference angles and their corresponding solutions in different quadrants.