vec(u)=(-1,4) 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 to find the direction angle. Vector u has components u = (-1, 4). The direction angle θ can be found using the arctangent function, where θ = arctan(y/x).Calculate Arctangent: Calculate the arctangent of the y-component divided by the x-component. θ = arctan(4/(-1)) = arctan(-4).Determine Correct Quadrant: Determine the correct quadrant for the angle. Since the x-component is negative and the y-component is positive, vector u lies in the second quadrant. The arctangent function will give us an angle in the fourth quadrant, so we need to add 180 degrees to get the angle in the second quadrant.Use Calculator for Arctangent: Use a calculator to find the arctangent of -4 and add 180 degrees to find the direction angle in the second quadrant. θ = arctan(-4) + 180° ≈ -75.96° + 180° ≈ 104.04°.Round Direction Angle: Round the direction angle to the nearest hundredth. θ ≈ 104.04° (rounded to the nearest hundredth).

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$\vec{u} = (-1,4)$ $\newline$ 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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Algebra 2

Find Coordinate on Unit Circle

Full solution

\vec{u} = (-1,4)

\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 to find the direction angle. $\newline$ Vector $u$ has components $u = (-1, 4)$ . The direction angle $\theta$ can be found using the arctangent function, where $\theta = \text{arctan}(\frac{y}{x})$ .
Calculate Arctangent: Calculate the arctangent of the y-component divided by the x-component. $\theta = \text{arctan}(\frac{4}{-1}) = \text{arctan}(-4)$ .
Determine Correct Quadrant: Determine the correct quadrant for the angle. $\newline$ Since the $x$ -component is negative and the $y$ -component is positive, vector $\mathbf{u}$ lies in the second quadrant. The arctangent function will give us an angle in the fourth quadrant, so we need to add $180$ degrees to get the angle in the second quadrant.
Use Calculator for Arctangent: Use a calculator to find the arctangent of $-4$ and add $180$ degrees to find the direction angle in the second quadrant. $\newline$ $\theta = \text{arctan}(-4) + 180° \approx -75.96° + 180° \approx 104.04°$ .
Round Direction Angle: Round the direction angle to the nearest hundredth. $\newline$ $\theta \approx 104.04^\circ$ (rounded to the nearest hundredth).