Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 17, 2023

Find the value of $\cot 80^{\circ}$ rounded to the nearest thousandth.

STEP 1

Assumptions1. We are asked to find the value of $\cot80^{\circ}$ to the nearest thousandth. . We know that $\cot \theta = \frac{1}{\tan \theta}$ .

STEP 2

We need to calculate the value of $\tan80^{\circ}$ first. $\tan80^{\circ}$

STEP 3

Using a scientific calculator, we find that $\tan80^{\circ} \approx5.671$

STEP 4

Now, we calculate the value of $\cot80^{\circ}$ using the formula $\cot \theta = \frac{1}{\tan \theta}$ .
$\cot80^{\circ} = \frac{1}{\tan80^{\circ}}$

STEP 5

Substitute the value of $\tan80^{\circ}$ into the equation.
$\cot80^{\circ} = \frac{1}{5.671}$

STEP 6

Calculate the value of $\cot80^{\circ}$ .
$\cot80^{\circ} \approx0.176$ So, the value of $\cot80^{\circ}$ to the nearest thousandth is0.176.

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