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Find the values of x that satisfy the equation 3sin(x) - 2 = 0.
Find the values of x that satisfy the equation 3sin(x) - 2 = 0.
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Practice Questions
1 question
Q1
Find the values of x that satisfy the equation 3sin(x) - 2 = 0.
π/6
5π/6
π/2
7π/6
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The solution is x = π/2.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the values of x that satisfy the equation 3sin(x) - 2 = 0.
Solution:
The solution is x = π/2.
Steps: 7
Show Steps
Step 1: Start with the equation 3sin(x) - 2 = 0.
Step 2: Add 2 to both sides of the equation to isolate the sine term: 3sin(x) = 2.
Step 3: Divide both sides by 3 to solve for sin(x): sin(x) = 2/3.
Step 4: Use the inverse sine function to find x: x = arcsin(2/3).
Step 5: Calculate the value of arcsin(2/3) to find the principal value of x.
Step 6: Remember that sine is positive in the first and second quadrants, so find the second solution: x = π - arcsin(2/3).
Step 7: The general solutions can be expressed as x = arcsin(2/3) + 2kπ and x = π - arcsin(2/3) + 2kπ, where k is any integer.
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