Select the answer which is equivalent to the given expression using your calculator. tan A=(9)/(40) and A is in Quadrant I. Find sin 2A. (360)/(1681) (720)/(1681) (3038)/(1681) (1519)/(1681)

Question

Select the answer which is equivalent to the given expression using your calculator.  tan A=(9)/(40) and A is in Quadrant I. Find  sin 2A.  (360)/(1681)  (720)/(1681)  (3038)/(1681)  (1519)/(1681)

Bytelearn · Accepted Answer

Define Tangent Ratio: We know that the tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle. Given tan A = 9/40, we can consider a right triangle where the opposite side (O) is 9 and the adjacent side (A) is 40. We need to find the hypotenuse (H) using the Pythagorean theorem: O^2 + A^2 = H^2.Calculate Hypotenuse: Calculate the hypotenuse (H) using the Pythagorean theorem: H^2 = O^2 + A^2. H^2 = 9^2 + 40^2 H^2 = 81 + 1600 H^2 = 1681 H = sqrt(1681) H = 41Find Sin and Cos: Now that we have the lengths of all sides of the right triangle, we can find sin A and cos A. Sin A is the ratio of the opposite side to the hypotenuse, and cos A is the ratio of the adjacent side to the hypotenuse. sin A = O/H = 9/41 cos A = A/H = 40/41Use Double Angle Formula: We need to find sin 2A. The double angle formula for sine is sin 2A = 2 * sin A * cos A. Let's use the values we found for sin A and cos A. sin 2A = 2 * (9/41) * (40/41)Multiply Values: Now, multiply the values to find sin 2A. sin 2A = 2 * (9/41) * (40/41) sin 2A = (2 * 9 * 40) / (41 * 41) sin 2A = (720) / (1681)Final Result: The value of sin 2A is 720/1681. This matches one of the answer choices provided.

Select the answer which is equivalent to the given expression using your calculator. $\tan A=\frac{9}{40}$ and A is in Quadrant I. $\newline$ Find $\sin 2 A$ . $\newline$ $\frac{360}{1681}$ $\newline$ $\frac{720}{1681}$ $\newline$ $\frac{3038}{1681}$ $\newline$ $\frac{1519}{1681}$

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