The angle theta_(1) is located in Quadrant III, and cos(theta_(1))=-(13)/(30). What is the value of sin(theta_(1)) ? Express your answer exactly. sin(theta_(1))=

Apply Pythagorean identity: Use the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 to find sin(theta_(1)). Since we know cos(theta_(1))=-(13)/(30), we can substitute this into the identity. sin^2(theta_(1)) + (-13/30)^2 = 1Solve for sin^2(theta_(1)): Simplify the equation to solve for sin^2(theta_(1)). sin^2(theta_(1)) + (169/900) = 1 sin^2(theta_(1)) = 1 - (169/900) sin^2(theta_(1)) = (900/900) - (169/900) sin^2(theta_(1)) = (731/900)Find sin(theta_(1)): Take the square root of both sides to find sin(theta_(1)). Since theta_(1) is in Quadrant III, sin(theta_(1)) will be negative (in Quadrant III, both sine and cosine are negative). sin(theta_(1)) = -sqrt(731/900) sin(theta_(1)) = -sqrt(731)/sqrt(900) sin(theta_(1)) = -sqrt(731)/30

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The angle
theta_(1) is located in Quadrant III, and
cos(theta_(1))=-(13)/(30).
What is the value of
sin(theta_(1)) ? Express your answer exactly.

sin(theta_(1))=

The angle $\theta_{1}$ is located in Quadrant III, and $\cos \left(\theta_{1}\right)=-\frac{13}{30}$ . $\newline$ What is the value of $\sin \left(\theta_{1}\right)$ ? Express your answer exactly. $\newline$ $\sin \left(\theta_{1}\right)=$

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Q. The angle

\theta_{1}

is located in Quadrant III, and

\cos \left(\theta_{1}\right)=-\frac{13}{30}

\newline

What is the value of

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

? Express your answer exactly.

\newline

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

Apply Pythagorean identity: Use the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$ to find $\sin(\theta_{1})$ . Since we know $\cos(\theta_{1})=-\frac{13}{30}$ , we can substitute this into the identity. $\sin^2(\theta_{1}) + \left(-\frac{13}{30}\right)^2 = 1$
Solve for $\sin^2(\theta_{1})$ : Simplify the equation to solve for $\sin^2(\theta_{1})$ . $\sin^2(\theta_{1}) + \frac{169}{900} = 1$ $\sin^2(\theta_{1}) = 1 - \frac{169}{900}$ $\sin^2(\theta_{1}) = \frac{900}{900} - \frac{169}{900}$ $\sin^2(\theta_{1}) = \frac{731}{900}$
Find $\sin(\theta_{1})$ : Take the square root of both sides to find $\sin(\theta_{1})$ . Since $\theta_{1}$ is in Quadrant III, $\sin(\theta_{1})$ will be negative (in Quadrant III, both sine and cosine are negative). $\sin(\theta_{1}) = -\sqrt{731/900}$ $\sin(\theta_{1}) = -\sqrt{731}/\sqrt{900}$ $\sin(\theta_{1}) = -\sqrt{731}/30$