Question 8
Difficulty: Ill
How many solutions, on the interval $] 0, 2 π [$ , are there for the equation, $| \tan θ | = 1$ ?
12
24
36
40

Answer

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Answer

$4$ solutions for the equation $| \tan θ | = 1$ in the interval $(0, 2 π)$

Steps

Step 1 ：Find the solutions for the equation $\tan θ = 1$ and $\tan θ = - 1$ in the interval $(0, 2 π)$

Step 2 ： $\tan θ = 1$ when $θ = \frac{π}{4} + n π$ and $\tan θ = - 1$ when $θ = \frac{3 π}{4} + n π$ , where n is an integer

Step 3 ：Find the solutions that fall within the given interval:

Step 4 ：solutions_1 = $[\frac{π}{4}, \frac{5 π}{4}]$

Step 5 ：solutions_2 = $[\frac{3 π}{4}, \frac{7 π}{4}]$

Step 6 ：total_solutions = 4

Step 7 ： $4$ solutions for the equation $| \tan θ | = 1$ in the interval $(0, 2 π)$