vec(u)=(-2,5) 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 Formula: Identify the formula for the direction angle of a vector. The direction angle theta of a vector vec(u)=(x,y) can be found using the arctangent function: theta = arctan(y/x). However, since arctan only gives values from -90^(@) to 90^(@), we need to adjust the angle based on the quadrant in which the vector lies.Calculate Arctangent: Calculate the arctangent of the y-coordinate divided by the x-coordinate. For vec(u)=(-2,5), we have x=-2 and y=5. Thus, theta = arctan(5/(-2)) = arctan(-2.5). Using a calculator, we find that arctan(-2.5) ≈ -68.20^(@).Adjust Based on Quadrant: Adjust the angle based on the quadrant. Since the x-coordinate is negative and the y-coordinate is positive, vec(u) lies in the second quadrant. In the second quadrant, we must add 180^(@) to the arctangent value to find the correct direction angle. Therefore, theta = -68.20^(@) + 180^(@) = 111.80^(@).Ensure Angle Range: Ensure the angle is within the range 0^(@) to 360^(@). The calculated angle, 111.80^(@), is already within the desired range. Therefore, no further adjustments are needed.

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$\vec{u} = (-2,5)$ $\newline$ 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

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\vec{u} = (-2,5)

\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 Formula: Identify the formula for the direction angle of a vector. The direction angle $\theta$ of a vector $\vec{u}=(x,y)$ can be found using the arctangent function: $\theta = \text{arctan}(\frac{y}{x})$ . However, since $\text{arctan}$ only gives values from $-90^{\circ}$ to $90^{\circ}$ , we need to adjust the angle based on the quadrant in which the vector lies.
Calculate Arctangent: Calculate the arctangent of the y-coordinate divided by the x-coordinate. $\newline$ For $\vec{u}=(-2,5)$ , we have $x=-2$ and $y=5$ . Thus, $\theta = \arctan\left(\frac{5}{-2}\right) = \arctan(-2.5)$ . $\newline$ Using a calculator, we find that $\arctan(-2.5) \approx -68.20^\circ$ .
Adjust Based on Quadrant: Adjust the angle based on the quadrant. $\newline$ Since the x-coordinate is negative and the y-coordinate is positive, $\vec{u}$ lies in the second quadrant. In the second quadrant, we must add $180^{\circ}$ to the arctangent value to find the correct direction angle. $\newline$ Therefore, $\theta = -68.20^{\circ} + 180^{\circ} = 111.80^{\circ}$ .
Ensure Angle Range: Ensure the angle is within the range $0^{\circ}$ to $360^{\circ}$ . The calculated angle, $111.80^{\circ}$ , is already within the desired range. Therefore, no further adjustments are needed.