Find the exact value of $s$ in the given interval that has the given circular function value. Do not use a calculator.
$[π, \frac{3 π}{2}]; \tan s = \frac{\sqrt{3}}{3}$
$s =$
radians
(Simplify your answer. Type an exact answer, using $π$ as needed. Use integers or fractions for any numbers in the expression.)

Answer

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Answer

$The exact value of s in the given interval that has the given circular function value is \frac{7 π}{6} radians.$

Steps

Step 1 ：The tangent function is positive in the first and third quadrants. The interval given, $[π, \frac{3 π}{2}]$ , is in the third quadrant.

Step 2 ：The value of $\tan s = \frac{\sqrt{3}}{3}$ corresponds to an angle of $\frac{π}{6}$ in the first quadrant.

Step 3 ：However, since we are in the third quadrant, we need to add $π$ to this angle to get the corresponding angle in the third quadrant.

Step 4 ： $first_quadrant_angle = \frac{π}{6}$

Step 5 ： $third_quadrant_angle = \frac{7 π}{6}$

Step 6 ： $The exact value of s in the given interval that has the given circular function value is \frac{7 π}{6} radians.$