Question

Please help me....Use the Pythagorean identity

Answer 1

Using the Pythagorean identity, the value of the cosine ratio is $\cos(\theta_1) = \frac{84}{85}$

How to determine the cosine ratio?

The given parameter is:

$\sin(\theta_1) = -\frac{13}{85}$

By the Pythagorean identity, we have:

$\sin^2(\theta_1) + \cos^2(\theta_1) = 1$

So, we have:

$(-\frac{13}{85})^2 + \cos^2(\theta_1) = 1$

This gives

$\cos^2(\theta_1) = 1 - (-\frac{13}{85})^2$

Evaluate

$\cos^2(\theta_1) = 1 - \frac{169}{7225}$

Take LCM

$\cos^2(\theta_1) = \frac{7225 -169}{7225}$

This gives

$\cos^2(\theta_1) = \frac{7056}{7225}$

Take the square root of both sides

$\cos(\theta_1) = \pm \frac{84}{85}$

Cosine is positive in the fourth quadrant.

So, we have:

$\cos(\theta_1) = \frac{84}{85}$

Hence, the cosine value is $\cos(\theta_1) = \frac{84}{85}$

Read more about Pythagorean identity at:

brainly.com/question/1969941

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