The angle theta_(1) is located in Quadrant I, and sin(theta_(1))=(17)/(20). What is the value of cos(theta_(1)) ? Express your answer exactly. cos(theta_(1))=

Step 1: Substitute sin(theta_(1)) in the Pythagorean identity: We know that sin(theta_(1)) = 17/20. Use the Pythagorean identity sin²(theta) + cos²(theta) = 1 to find the value of cos(theta_(1)). Substitute 17/20 for sin(theta_(1)) in sin²(theta) + cos²(theta) = 1. (17/20)² + cos²(theta_(1)) = 1.Step 2: Simplify the equation: Simplify (17/20)² + cos²(theta_(1)) = 1 to find the value of cos²(theta_(1)). (17/20)² = 289/400. cos²(theta_(1)) = 1 - 289/400. cos²(theta_(1)) = 400/400 - 289/400. cos²(theta_(1)) = 111/400.Step 3: Calculate cos²(theta_(1)): Since theta_(1) is in Quadrant I, where all trigonometric functions are positive, cos(theta_(1)) will be positive. Therefore, cos(theta_(1)) = sqrt(111/400). cos(theta_(1)) = sqrt(111)/sqrt(400). cos(theta_(1)) = sqrt(111)/20.

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The angle
theta_(1) is located in Quadrant I, and
sin(theta_(1))=(17)/(20).
What is the value of
cos(theta_(1)) ? Express your answer exactly.

cos(theta_(1))=

The angle $\theta_{1}$ is located in Quadrant I, and $\sin \left(\theta_{1}\right)=\frac{17}{20}$ . $\newline$ 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 I, and

\sin \left(\theta_{1}\right)=\frac{17}{20}

\newline

What is the value of

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

? Express your answer exactly.

\newline

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

Step $1$ : Substitute $\sin(\theta_{1})$ in the Pythagorean identity: We know that $\sin(\theta_{1}) = \frac{17}{20}$ . Use the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$ to find the value of $\cos(\theta_{1})$ . $\newline$ Substitute $\frac{17}{20}$ for $\sin(\theta_{1})$ in $\sin^2(\theta) + \cos^2(\theta) = 1$ . $\newline$ $\left(\frac{17}{20}\right)^2 + \cos^2(\theta_{1}) = 1$ .
Step $2$ : Simplify the equation: Simplify $(\frac{17}{20})^2 + \cos^2(\theta_{1}) = 1$ to find the value of $\cos^2(\theta_{1})$ . $(\frac{17}{20})^2 = \frac{289}{400}.$ $\cos^2(\theta_{1}) = 1 - \frac{289}{400}.$ $\cos^2(\theta_{1}) = \frac{400}{400} - \frac{289}{400}.$ $\cos^2(\theta_{1}) = \frac{111}{400}.$
Step $3$ : Calculate $\cos^2(\theta_1)$ : Since $\theta_1$ is in Quadrant I, where all trigonometric functions are positive, $\cos(\theta_1)$ will be positive. $\newline$ Therefore, $\cos(\theta_1) = \sqrt{\frac{111}{400}}$ . $\newline$ $\cos(\theta_1) = \frac{\sqrt{111}}{\sqrt{400}}$ . $\newline$ $\cos(\theta_1) = \frac{\sqrt{111}}{20}$ .