Hello, could somebody please help me out with the following question? I would greatly appreciate some assistance.
Find all values of x in the interval [0, 2π] that satisfy the equation
3|tanx(x)|=3
well, you want
|tan(x)| = 1
tanx = 1 or -1
you know that tan π/4 = 1
so use that as your reference angle. The rest is easy.
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right?
Steve, wouldn't I consider only the values for tanx=1 given the interval restriction?
Never mind, I understand it now. Thank you for your help, Steve.
no
|-1| = 1
I don't agree with dat ansa . . |tanx|=1 . . X =tan inverse of 1 which is 45 . .the ansa 4 x is 45
Of course! I'd be happy to help you solve this equation.
To find the values of x that satisfy the equation, we will begin by isolating the absolute value expression:
3|tan(x)| = 3
Dividing both sides of the equation by 3 gives us:
|tan(x)| = 1
Next, recall that the absolute value of a number is equal to the number itself if the number is positive, and the negative of the number if the number is negative. Therefore, we have two cases to consider:
Case 1: tan(x) = 1
In this case, we need to find all x-values in the interval [0, 2π] that satisfy the equation tan(x) = 1. One solution in that interval is π/4. However, note that the tangent function is periodic with a period of π, which means that it repeats every π radians. Therefore, we can add π to the solution found, giving us a second solution of 5π/4.
Case 2: tan(x) = -1
Similarly, we need to find all x-values in the interval [0, 2π] that satisfy the equation tan(x) = -1. One solution in that interval is 3π/4, and adding π gives us a second solution of 7π/4.
So, the values of x in the interval [0, 2π] that satisfy the equation 3|tan(x)| = 3 are π/4, 3π/4, 5π/4, and 7π/4.
I hope this explanation helps! Let me know if you have any further questions.