The angle theta_(1) is located in Quadrant IV, and sin(theta_(1))=-(13)/(85). What is the value of cos(theta_(1)) ? Express your answer exactly. cos(theta_(1))=

Apply Pythagorean identity: Use the Pythagorean identity for sine and cosine. The Pythagorean identity states that sin^2(θ) + cos^2(θ) = 1. We know sin(theta_(1)) = -(13)/(85), so we can find cos^2(theta_(1)) using the identity.Calculate cos^2(theta_(1)): Calculate cos^2(theta_(1)). sin^2(theta_(1)) = (-(13)/(85))^2 sin^2(theta_(1)) = (169)/(7225) cos^2(theta_(1)) = 1 - sin^2(theta_(1)) cos^2(theta_(1)) = 1 - (169)/(7225) cos^2(theta_(1)) = (7225)/(7225) - (169)/(7225) cos^2(theta_(1)) = (7056)/(7225)Find cos(theta_(1)): Take the square root of cos^2(theta_(1)) to find cos(theta_(1)). Since theta_(1) is in Quadrant IV, cosine is positive. cos(theta_(1)) = sqrt((7056)/(7225)) cos(theta_(1)) = (84)/(85)

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The angle
theta_(1) is located in Quadrant IV, and
sin(theta_(1))=-(13)/(85).
What is the value of
cos(theta_(1)) ? Express your answer exactly.

cos(theta_(1))=

The angle $\theta_{1}$ is located in Quadrant IV, and $\sin \left(\theta_{1}\right)=-\frac{13}{85}$ . $\newline$ What is the value of $\cos \left(\theta_{1}\right)$ ? Express your answer exactly. $\newline$ $\cos \left(\theta_{1}\right)=$

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Q. The angle

\theta_{1}

is located in Quadrant IV, and

\sin \left(\theta_{1}\right)=-\frac{13}{85}

\newline

What is the value of

\cos \left(\theta_{1}\right)

? Express your answer exactly.

\newline

\cos \left(\theta_{1}\right)=

Apply Pythagorean identity: Use the Pythagorean identity for sine and cosine. $\newline$ The Pythagorean identity states that $\sin^2(\theta) + \cos^2(\theta) = 1$ . $\newline$ We know $\sin(\theta_{1}) = -\frac{13}{85}$ , so we can find $\cos^2(\theta_{1})$ using the identity.
Calculate $\cos^2(\theta_{1})$ : Calculate $\cos^2(\theta_{1})$ .
$\sin^2(\theta_{1}) = \left(-\frac{13}{85}\right)^2$
$\sin^2(\theta_{1}) = \frac{169}{7225}$
$\cos^2(\theta_{1}) = 1 - \sin^2(\theta_{1})$
$\cos^2(\theta_{1}) = 1 - \frac{169}{7225}$
$\cos^2(\theta_{1}) = \frac{7225}{7225} - \frac{169}{7225}$
$\cos^2(\theta_{1}) = \frac{7056}{7225}$
Find $\cos(\theta_{1})$ : Take the square root of $\cos^2(\theta_{1})$ to find $\cos(\theta_{1})$ . $\newline$ Since $\theta_{1}$ is in Quadrant IV, cosine is positive. $\newline$ $\cos(\theta_{1}) = \sqrt{\frac{7056}{7225}}$ $\newline$ $\cos(\theta_{1}) = \frac{84}{85}$