Find the general solution of the equation sin(x) = -1/2.
Practice Questions
1 question
Q1
Find the general solution of the equation sin(x) = -1/2.
x = 7π/6 + 2nπ
x = 11π/6 + 2nπ
x = 7π/6, 11π/6
Both 1 and 2
The general solutions are x = 7π/6 + 2nπ and x = 11π/6 + 2nπ.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the general solution of the equation sin(x) = -1/2.
Solution: The general solutions are x = 7π/6 + 2nπ and x = 11π/6 + 2nπ.
Steps: 6
Step 1: Understand the equation sin(x) = -1/2. We need to find the angles x where the sine value is -1/2.
Step 2: Recall the unit circle. The sine function is negative in the third and fourth quadrants.
Step 3: Identify the reference angle. The reference angle for sin(x) = 1/2 is π/6 (30 degrees).
Step 4: Find the angles in the third and fourth quadrants where sine is -1/2. These angles are: π + π/6 = 7π/6 (third quadrant) and 2π - π/6 = 11π/6 (fourth quadrant).
Step 5: Write the general solutions. Since sine is periodic with a period of 2π, we add 2nπ (where n is any integer) to each solution.
Step 6: Combine the results. The general solutions are x = 7π/6 + 2nπ and x = 11π/6 + 2nπ.
