vec(u)=(4,-2) Find the direction angle of vec(u). Enter your answer as an angle in degrees between 0^(@) and 360^(@) rounded to the nearest hundredth. theta=◻^(@)

Identify Components and Formula: Identify the components of vector u and the formula for the direction angle. Vector u has components u = (4, -2). The direction angle θ of a vector can be found using the arctangent function, specifically θ = arctan(y/x) where x and y are the components of the vector.Calculate Arctangent: Calculate the arctangent of the y-component divided by the x-component. θ = arctan((-2)/4) = arctan(-0.5)Use Calculator for Value: Use a calculator to find the value of θ in radians. θ ≈ arctan(-0.5) ≈ -0.463647609 radiansConvert Radians to Degrees: Convert the angle from radians to degrees. θ ≈ -0.463647609 radians × (180/π) degrees/radian ≈ -26.56505118 degreesAdjust Negative Angle: Since the angle is negative and we want an angle between 0 and 360 degrees, add 360 degrees to the calculated angle. θ ≈ -26.56505118 degrees + 360 degrees ≈ 333.4349488 degreesRound to Nearest Hundredth: Round the direction angle to the nearest hundredth. θ ≈ 333.43 degrees

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$\vec{u}=(4,-2)$ $\newline$ Find the direction angle of $\vec{u}$ . $\newline$ Enter your answer as an angle in degrees between $0^\circ$ and $360^\circ$ rounded to the nearest hundredth. $\newline$ $\theta = \square^\circ$

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Math Problems

Algebra 2

Find Coordinate on Unit Circle

Full solution

\vec{u}=(4,-2)

\newline

Find the direction angle of

\vec{u}

\newline

Enter your answer as an angle in degrees between

0^\circ

and

360^\circ

rounded to the nearest hundredth.

\newline

\theta = \square^\circ

Identify Components and Formula: Identify the components of vector $u$ and the formula for the direction angle. $\newline$ Vector $u$ has components $u = (4, -2)$ . The direction angle $\theta$ of a vector can be found using the arctangent function, specifically $\theta = \text{arctan}(y/x)$ where $x$ and $y$ are the components of the vector.
Calculate Arctangent: Calculate the arctangent of the $y$ -component divided by the $x$ -component. $\theta = \arctan\left(\frac{-2}{4}\right) = \arctan(-0.5)$
Use Calculator for Value: Use a calculator to find the value of $\theta$ in radians. $\newline$ $\theta \approx \arctan(-0.5) \approx -0.463647609$ radians
Convert Radians to Degrees: Convert the angle from radians to degrees. $\theta \approx -0.463647609$ radians $\times (\frac{180}{\pi})$ degrees/radian $\approx -26.56505118$ degrees
Adjust Negative Angle: Since the angle is negative and we want an angle between $0$ and $360$ degrees, add $360$ degrees to the calculated angle. $\newline$ $\theta \approx -26.56505118$ degrees $+ 360$ degrees $\approx 333.4349488$ degrees
Round to Nearest Hundredth: Round the direction angle to the nearest hundredth. $\theta \approx 333.43$ degrees