Question

use a calculator to find a decimal approximation for the given value.
\\(\frac{1}{\cot 56.5^\circ}\\)

\\(\frac{1}{\cot 56.5^\circ} \approx \square\\)
(round to seven decimal places as needed.)

Explanation:

Step1: Recall the reciprocal identity of cotangent

We know that \(\frac{1}{\cot\theta}=\tan\theta\), so \(\frac{1}{\cot56.5^{\circ}}=\tan56.5^{\circ}\).

Step2: Use a calculator to find \(\tan56.5^{\circ}\)

Make sure the calculator is in degree mode. Then calculate \(\tan(56.5)\). Using a calculator, we get \(\tan(56.5^{\circ})\approx1.5193300\) (rounded to seven decimal places).

Answer:

\(1.5193300\)