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State whether the following equation have solution or not? 3 tanθ = 5 - Mathematics and Statistics

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Question

State whether the following equation have solution or not?

3 tanθ = 5

Sum
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Solution

Yes, it has a solution.

Because tanθ can take any real value, from

3 tanθ = 5 ⇒ tanθ = `5/3`, which is possible

θ = tan−1 `(5/3) + npi,` n ∈ Z

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Trigonometric Equations and Their Solutions
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Chapter 3: Trigonometric Functions - Exercise 3.1 [Page 75]

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