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3 years ago

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https://www.usatestprep.com/modules/questions/qq.php?testid=913&assignment_id=45614607&strand=7060&element=35103&amp

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torisob [31]3 years ago

5 0

Have a nice day be safe

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D) all real numbers

Step-by-step explanation:

The domain is the input values, in this case the x values

What x values can we use

x goes from - infinity to plus infinity, so it is all real numbers

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3 years ago

Find the exact value of cot 330° in simplest form with a rational denominator.

Hoochie [10]

Answer:

$\cot 330^{\circ} = -\sqrt{3}$

Step-by-step explanation:

The cotangent function can be rewritten by trigonometric relations, that is:

$\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}$ (1)

By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:

$\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}$ (2)

$\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}$ (3)

By (2) and (3) in (1), we have following expression:

$\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}$

If we know that $\sin 30^{\circ} = \frac{1}{2}$ and $\cos 30^{\circ} = \frac{\sqrt{3}}{2}$ , then the result of the trigonometric expression is:

$\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }$

$\cot 330^{\circ} = -\sqrt{3}$

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3 years ago