vec(u)=(-4,-3) 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 (-4, -3). The direction angle θ of a vector (x, y) can be found using the arctangent function: θ = atan2(y, x).Calculate Direction Angle: Calculate the direction angle using the arctangent function. θ = atan2(-3, -4). The atan2 function takes into account the signs of both vector components to determine the correct quadrant for the angle.Use Calculator for Value: Use a calculator to find the value of θ. θ = atan2(-3, -4) ≈ 213.69 degrees. This is the angle in the standard position, measured counterclockwise from the positive x-axis.Check Angle Range: Check if the angle is within the range of 0 to 360 degrees. Since 213.69 degrees is within the range of 0 to 360 degrees, no further adjustments are needed.

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$\vec{u} = (-4, -3)$ $\newline$ 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} = (-4, -3)

\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 $(-4, -3)$ . The direction angle $\theta$ of a vector $(x, y)$ can be found using the arctangent function: $\theta = \text{atan2}(y, x)$ .
Calculate Direction Angle: Calculate the direction angle using the arctangent function. $\theta = \text{atan2}(-3, -4)$ . The atan $2$ function takes into account the signs of both vector components to determine the correct quadrant for the angle.
Use Calculator for Value: Use a calculator to find the value of $\theta$ . $\theta = \text{atan2}(-3, -4) \approx 213.69$ degrees. This is the angle in the standard position, measured counterclockwise from the positive x-axis.
Check Angle Range: Check if the angle is within the range of $0$ to $360$ degrees. $\newline$ Since $213.69$ degrees is within the range of $0$ to $360$ degrees, no further adjustments are needed.