Find all solutions for the following equation in the interval
0 ≤ x <2pi
3cos(3x)=6
i got cos3x=2, don't know how to go further i think it would be no solution but just want to confirm.
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You are right, there is no solution
cos(of any angle) must be between -1 and +1
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To solve the equation 3cos(3x) = 6 in the interval 0 ≤ x < 2π, follow these steps:
1. Divide both sides of the equation by 3: cos(3x) = 2.
2. Since the range of the cosine function is -1 to 1, there are no values of x that satisfy the equation cos(3x) = 2. Therefore, there are no solutions in the given interval.
To confirm, you can use a graphing calculator or a computer program to graph the function y = 3cos(3x) - 6 and see that it does not intersect the x-axis in the interval 0 ≤ x < 2π.