What are the solutions of the equation sin(x) = sin(π/3)?
Practice Questions
1 question
Q1
What are the solutions of the equation sin(x) = sin(π/3)?
x = π/3
x = 2π/3
x = 4π/3
x = 5π/3
The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.
Questions & Step-by-step Solutions
1 item
Q
Q: What are the solutions of the equation sin(x) = sin(π/3)?
Solution: The solutions are x = π/3 + 2nπ and x = 2π/3 + 2nπ.
Steps: 6
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.
