- #1
Nyasha
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Homework Statement
Find all solutions to the following equation: [tex]3tan(Inx)=2[/tex]
The Attempt at a Solution
[tex]tan(Inx)=2/3[/tex]
[tex]Inx=arctan(2/3)[/tex]
x=e^(arctan(2/3)
Last edited:
lanedance said:Hi Nyasha
i think you mean ln(x) = arctan(2/3)?
lanedance said:think about a graph of the function
y = tanx
it basically repeats along the axis every 2.pi
when you take the arctan, you can think of it as picking a y value, tracing it out to across to where it intersects the curve, and dropping down to the x value, giving you
x = arctan(y)
how do you choose a curve to use...? multiple solutions... how many are there?
An inverse tangent equation is an equation in which the input is the tangent of an angle and the output is the angle itself. In other words, it is the opposite of the tangent function and can help us find the measure of an angle when given its tangent value.
To solve an inverse tangent equation, we need to use a calculator or a table to find the inverse tangent of the given tangent value. Once we have the inverse tangent value, we can use the inverse property of tangent to find the angle that produces that value.
This equation means that the tangent of an angle, when multiplied by 3 and then taken the natural logarithm of, will equal 2. In other words, the tangent of an angle is equal to 2 divided by 3, which is approximately 0.667.
Since this is an inverse tangent equation, there are an infinite number of solutions. The tangent function repeats itself every 360 degrees, so we can find multiple angles that have the same tangent value.
To find all solutions to this equation, we need to use a general formula that takes into account the periodic nature of the tangent function. In this specific equation, there are an infinite number of solutions, so it is best to use a calculator or a graphing tool to visualize and find the solutions.