use a calculator to find the value of the trigonometric function.\n\n\\( \\cot \\frac { 5 \\pi } { 12 }…

use a calculator to find the value of the trigonometric function.\n\n\\( \\cot \\frac { 5 \\pi } { 12 } \\)\n\n\\( \\cot \\frac { 5 \\pi } { 12 } \\approx \\square \\) (round to four decimal places as needed.)

use a calculator to find the value of the trigonometric function.\n\n\\( \\cot \\frac { 5 \\pi } { 12 } \\)\n\n\\( \\cot \\frac { 5 \\pi } { 12 } \\approx \\square \\) (round to four decimal places as needed.)

Answer

Explanation:

Step1: Use the reciprocal identity

Since (\cot\theta=\frac{1}{\tan\theta}), then (\cot\frac{5\pi}{12}=\frac{1}{\tan\frac{5\pi}{12}}).

Step2: Calculate (\tan\frac{5\pi}{12})

Using a calculator in radian mode, (\tan\frac{5\pi}{12}\approx3.73205080757).

Step3: Calculate (\cot\frac{5\pi}{12})

(\cot\frac{5\pi}{12}=\frac{1}{\tan\frac{5\pi}{12}}\approx\frac{1}{3.73205080757}\approx0.2679)

Answer:

(0.2679)