Select the answer which is equivalent to the given expression using your calculator. cos A=(30)/(50) and A is in Quadrant I. Find cos 2A. (2400)/(2500) (-350)/(2500) (-700)/(2500) (1200)/(2500)

Apply Double Angle Formula: First, we need to use the double angle formula for cosine, which is cos(2A) = 2cos^2(A) - 1. We know that cos A = 30/50, so we will substitute this value into the formula.Calculate cos^2(A): Calculate cos^2(A) by squaring the value of cos A. cos^2(A) = (30/50)^2 = (30^2)/(50^2) = 900/2500.Substitute into Formula: Now, we will plug the value of cos^2(A) into the double angle formula. cos(2A) = 2(900/2500) - 1.Multiply and Subtract: Multiply 2 by 900/2500 to get the first part of the expression. 2 * (900/2500) = 1800/2500.Final Result: Now, subtract 1 from 1800/2500. Since 1 is equivalent to 2500/2500, we will perform the subtraction as follows: 1800/2500 - 2500/2500 = -700/2500.We have found that cos(2A) = -700/2500. This matches one of the given answer choices.

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=(30)/(50) and A is in Quadrant I.
Find
cos 2A.

(2400)/(2500)

(-350)/(2500)

(-700)/(2500)

(1200)/(2500)

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\cos A=\frac{30}{50}$ and A is in Quadrant I. $\newline$ Find $\cos 2 A$ . $\newline$ $\frac{2400}{2500}$ $\newline$ $\frac{-350}{2500}$ $\newline$ $\frac{-700}{2500}$ $\newline$ $\frac{1200}{2500}$

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.

\newline

\cos A=\frac{30}{50}

and A is in Quadrant I.

\newline

Find

\cos 2 A

\newline

\frac{2400}{2500}

\newline

\frac{-350}{2500}

\newline

\frac{-700}{2500}

\newline

\frac{1200}{2500}

Apply Double Angle Formula: First, we need to use the double angle formula for cosine, which is $\cos(2A) = 2\cos^2(A) - 1$ . We know that $\cos A = \frac{30}{50}$ , so we will substitute this value into the formula.
Calculate $\cos^2(A)$ : Calculate $\cos^2(A)$ by squaring the value of $\cos A$ . $\newline$ $\cos^2(A) = \left(\frac{30}{50}\right)^2 = \left(\frac{30^2}{50^2}\right) = \frac{900}{2500}$ .
Substitute into Formula: Now, we will plug the value of $\cos^2(A)$ into the double angle formula. $\newline$ $\cos(2A) = 2(\frac{900}{2500}) - 1$ .
Multiply and Subtract: Multiply $2$ by $900/2500$ to get the first part of the expression. $\newline$ $2 \times (900/2500) = 1800/2500$ .
Final Result: Now, subtract $1$ from $1800/2500$ . Since $1$ is equivalent to $2500/2500$ , we will perform the subtraction as follows: $\newline$ $1800/2500 - 2500/2500 = -700/2500$ .
Final Result: Now, subtract $1$ from $1800/2500$ . Since $1$ is equivalent to $2500/2500$ , we will perform the subtraction as follows: $\newline$ $1800/2500 - 2500/2500 = -700/2500$ .We have found that $\cos(2A) = -700/2500$ . This matches one of the given answer choices.