The angle theta_(1) is located in Quadrant II, and cos(theta_(1))=-(22)/(29). What is the value of sin(theta_(1)) ? Express your answer exactly. sin(theta_(1))=

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The angle  theta_(1) is located in Quadrant II, and  cos(theta_(1))=-(22)/(29). What is the value of  sin(theta_(1)) ? Express your answer exactly.  sin(theta_(1))=

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Quadrant II and Pythagorean Identity: We know that in Quadrant II, the sine function is positive, and we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find the value of sin(θ).Substituting cos(theta_(1)) into the Identity: First, we substitute the given value of cos(theta_(1)) into the Pythagorean identity. sin^2(theta_(1)) + (-22/29)^2 = 1Calculating the Square of cos(theta_(1)): Next, we calculate the square of cos(theta_(1)). (-22/29)^2 = 484/841Substituting the Value Back into the Identity: Now, we substitute this value back into the Pythagorean identity. sin^2(theta_(1)) + 484/841 = 1Solving for sin^2(theta_(1)): We then solve for sin^2(theta_(1)). sin^2(theta_(1)) = 1 - 484/841Subtracting the Fraction from 1: Subtracting the fraction from 1 gives us: sin^2(theta_(1)) = 841/841 - 484/841Simplifying the Subtraction: Simplifying the subtraction, we get: sin^2(theta_(1)) = (841 - 484) / 841Performing the Subtraction in the Numerator: Performing the subtraction in the numerator gives us: sin^2(theta_(1)) = 357 / 841Taking the Positive Square Root: Since we are looking for sin(theta_(1)) and we know it should be positive in Quadrant II, we take the positive square root of the result. sin(theta_(1)) = sqrt(357 / 841)Simplifying the Square Root: Simplifying the square root, we find that 841 is a perfect square, being 29^2, so: sin(theta_(1)) = sqrt(357) / 29

The angle $\theta_{1}$ is located in Quadrant II, and $\cos \left(\theta_{1}\right)=-\frac{22}{29}$ . $\newline$ What is the value of $\sin \left(\theta_{1}\right)$ ? Express your answer exactly. $\newline$ $\sin \left(\theta_{1}\right)=$

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