Select the answer which is equivalent to the given expression using your calculator. cos A=(11)/(61) and A is in Quadrant I. Find cos 2A. (660)/(3721) (-6958)/(3721) (-3479)/(3721) (1320)/(3721)

Question

Select the answer which is equivalent to the given expression using your calculator.  cos A=(11)/(61) and A is in Quadrant I. Find  cos 2A.  (660)/(3721)  (-6958)/(3721)  (-3479)/(3721)  (1320)/(3721)

Bytelearn · Accepted Answer

Apply Double Angle Formula: We will use the double angle formula for cosine, which is cos(2A) = 2cos^2(A) - 1 or cos(2A) = 1 - 2sin^2(A). Since we are given cos(A) and A is in Quadrant I where all trigonometric functions are positive, we can use the first formula.Square Cos(A): First, we square the value of cos(A) to find cos^2(A).  cos^2(A) = (11/61)^2 = 121/3721.Calculate 2cos^2(A): Next, we multiply this value by 2 to find 2cos^2(A). 2cos^2(A) = 2 * (121/3721) = 242/3721.Use Double Angle Formula: Now, we apply the double angle formula for cosine: cos(2A) = 2cos^2(A) - 1. cos(2A) = 242/3721 - 1.Subtract 1: To subtract 1 from 242/3721, we need to express 1 as a fraction with the same denominator, which is 3721/3721. cos(2A) = 242/3721 - 3721/3721.Combine Fractions: Now, we subtract the numerators and keep the common denominator. cos(2A) = (242 - 3721) / 3721 = -3479/3721.Check Given Options: We check the given options to see if -3479/3721 matches any of them. The correct option is (-3479)/(3721).

Select the answer which is equivalent to the given expression using your calculator. $\cos A=\frac{11}{61}$ and A is in Quadrant I. $\newline$ Find $\cos 2 A$ . $\newline$ $\frac{660}{3721}$ $\newline$ $\frac{-6958}{3721}$ $\newline$ $\frac{-3479}{3721}$ $\newline$ $\frac{1320}{3721}$

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