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3 years ago

Here are four number cards.

Mathematics

1 answer:

yaroslaw [1]3 years ago

3 0

Answer:

a) 14

b) 514

Step-by-step explanation:

use number line for b

514 is 14 away from 500

485 is 15 away from 500

so 514 is closer to 500

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Find the exact value of cos(theta) for an angle (theta) with tan (theta)= -2/3 and with its terminal side in Quadrant II.

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Answer:

$-\frac{3\sqrt{13}}{13}$ .

Step-by-step explanation:

Since we are in quadrant two, cosine value is negative while sine value is positive.

We are going to use the Pythagorean Identity: $1+\tan^2(\theta)=\sec^2(\theta)$ .

$1+(\frac{-2}{3})^2=\sec^2(\theta)$

$1+\frac{4}{9}=\sec^2(\theta)$

$\frac{9+4}{9}=\sec^2(\theta)$

$\frac{13}{9}=\sec^2(\theta)$

$\pm \sqrt{\frac{13}{9}}=\sec(\theta)$

$\pm \frac{\sqrt{13}}{3}=\sec(\theta)$

Since cosine and secant are reciprocals then they will have the same sign as along as they both exist.

$\sec(\theta)=-\frac{\sqrt{13}}{3}$

$\cos(\theta)=-\frac{3}{\sqrt{13}}$ .

I don't see this answer as I'm going to rationalize the denominator.

$\cos(\theta)=-\frac{3}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$ .

$\cos(\theta)=-\frac{3\sqrt{13}}{13}$ .

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Answer:

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Step-by-step explanation:

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