Find the general solution of the equation sin(x) = sin(π/4).

Find the general solution of the equation sin(x) = sin(π/4).

Correct Answer: x = nπ + (-1)^n π/4

Step 1: Understand the equation sin(x) = sin(π/4). This means we are looking for all values of x where the sine of x equals the sine of π/4.
Step 2: Recall that sin(π/4) is a specific value. We know that sin(π/4) = √2/2.
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 general solutions for sin(x) = sin(a) can be expressed as x = nπ + (-1)^n a, where n is any integer and a is the angle we are comparing to (in this case, π/4).
Step 5: Substitute a with π/4 in the general solution formula: x = nπ + (-1)^n (π/4).
Step 6: This gives us the final general solution: x = nπ + (-1)^n π/4, where n is any integer.

Trigonometric Equations – The question tests the understanding of solving equations involving the sine function and finding general solutions.
Periodic Functions – It assesses knowledge of the periodic nature of the sine function and how to express solutions in terms of integer multiples of π.
General Solutions – The question evaluates the ability to derive general solutions that account for all possible angles that satisfy the equation.