Select the answer which is equivalent to the given expression using your calculator. cos A=(52)/(65) and A is in Quadrant I. Find cos 2A. (2366)/(4225) (4056)/(4225) (2028)/(4225) (1183)/(4225)

Apply Double Angle Formula: Use the double angle formula for cosine: cos(2A) = 2cos^2(A) - 1. Given cos A = 52/65, we can substitute this into the formula. cos(2A) = 2(52/65)^2 - 1.Calculate (52/65)^2: Calculate (52/65)^2 to simplify the expression. (52/65)^2 = (52^2)/(65^2) = 2704/4225.Substitute Value: Substitute the value back into the double angle formula. cos(2A) = 2(2704/4225) - 1.Multiply and Subtract: Multiply 2 by 2704/4225. 2 * 2704/4225 = 5408/4225.Perform Final Subtraction: Subtract 1 from 5408/4225. Since 1 is equivalent to 4225/4225, we will perform the subtraction as follows: 5408/4225 - 4225/4225 = (5408 - 4225)/4225.Perform the subtraction to find the value of cos(2A). (5408 - 4225)/4225 = 1183/4225.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select the answer which is equivalent to the given expression using your calculator.
cos A=(52)/(65) and A is in Quadrant I.
Find
cos 2A.

(2366)/(4225)

(4056)/(4225)

(2028)/(4225)

(1183)/(4225)

Select the answer which is equivalent to the given expression using your calculator. $\cos A=\frac{52}{65}$ and A is in Quadrant I. $\newline$ Find $\cos 2 A$ . $\newline$ $\frac{2366}{4225}$ $\newline$ $\frac{4056}{4225}$ $\newline$ $\frac{2028}{4225}$ $\newline$ $\frac{1183}{4225}$

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Select the answer which is equivalent to the given expression using your calculator.

\cos A=\frac{52}{65}

and A is in Quadrant I.

\newline

Find

\cos 2 A

\newline

\frac{2366}{4225}

\newline

\frac{4056}{4225}

\newline

\frac{2028}{4225}

\newline

\frac{1183}{4225}

Apply Double Angle Formula: Use the double angle formula for cosine: $\cos(2A) = 2\cos^2(A) - 1$ . Given $\cos A = \frac{52}{65}$ , we can substitute this into the formula. $\cos(2A) = 2\left(\frac{52}{65}\right)^2 - 1$ .
Calculate $(52/65)^2$ : Calculate $(52/65)^2$ to simplify the expression. $(52/65)^2 = (52^2)/(65^2) = 2704/4225$ .
Substitute Value: Substitute the value back into the double angle formula. $\newline$ $\cos(2A) = 2\left(\frac{2704}{4225}\right) - 1$ .
Multiply and Subtract: Multiply $2$ by $2704/4225$ . $\newline$ $2 \times 2704/4225 = 5408/4225$ .
Perform Final Subtraction: Subtract $1$ from $5408/4225$ . Since $1$ is equivalent to $4225/4225$ , we will perform the subtraction as follows: $\newline$ $5408/4225 - 4225/4225 = (5408 - 4225)/4225$ .
Perform Final Subtraction: Subtract $1$ from $5408/4225$ . Since $1$ is equivalent to $4225/4225$ , we will perform the subtraction as follows: $\newline$ $5408/4225 - 4225/4225 = (5408 - 4225)/4225$ .Perform the subtraction to find the value of $\cos(2A)$ . $\newline$ $(5408 - 4225)/4225 = 1183/4225$ .