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1 year ago

Need help. and original answer

Mathematics

1 answer:

siniylev [52]1 year ago

7 0

The inequality written in interval notation is therefore -4<x<-1 or (-4, -1)

<h3 /><h3>What are inequalities?</h3>

Inequalities are expressions separated by the mathematical inequalities ≤, ≥, < and >

For instance a < b is a form of inequality.

<h3>What is a number line?</h3>

A number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations.

From the given number line, we can see that closed circles are on -4 and -1. The inequality written in interval notation is therefore -4<x<-1 or (-4, -1)

Learn more on inequality here: brainly.com/question/24372553

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3 years ago

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Snowcat [4.5K]

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3 years ago

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3 years ago

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Cos(−θ)=√3/3, sinθ<0

Delicious77 [7]

Answer:

$\sin\theta=-\frac{\sqrt{6}}{3}$

Step-by-step explanation:

The given trigonometric equation is $\cos(-\theta)=\frac{\sqrt{3} }{3}$ .

We can either use the Pythagorean identity or the right angle triangle to solve for $\sin\theta$ .

According to the Pythagorean identity,

$\cos^2\theta+\sin^2\theta=1$

Recall that, the cosine function is an even function, therefore

$\cos(-\theta)=\cos(\theta)$

$\Rightarrow \cos(\theta)=\frac{\sqrt{3} }{3}$ .

We substitute this value in to the above Pythagorean identity to get;

$(\frac{\sqrt{3}}{3})^2+\sin^2\theta=1$

$\Rightarrow \frac{3}{9}+\sin^2\theta=1$

$\Rightarrow \sin^2\theta=1-\frac{3}{9}$

$\Rightarrow \sin^2\theta=\frac{6}{9}$

$\Rightarrow \sin\theta=\pm \sqrt{\frac{6}{9}}$

$\Rightarrow \sin\theta=\pm \frac{\sqrt{6}}{3}$

But we were given that,

$\sin\theta\:$ , so we choose the negative value.

$\Rightarrow \sin\theta=-\frac{\sqrt{6}}{3}$

The correct answer is B

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3 years ago