vec(u)=(7,-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 the vector u and the formula to find the direction angle. Vector u has components u = (7, -4). The direction angle θ of a vector can be found using the arctangent function, where θ = arctan(y/x) for a vector with components (x, y).Calculate Arctangent: Calculate the arctangent of the y-component divided by the x-component to find the direction angle in radians. θ = arctan((-4)/7)Use Calculator for Value: Use a calculator to find the arctangent value. θ = arctan((-4)/7) ≈ -29.74 degrees (in radians, this would be approximately -0.5191 radians)Adjust for Quadrant: Since the vector is in the fourth quadrant (x is positive and y is negative), we need to add 360 degrees to the angle to find the direction angle between 0 and 360 degrees. θ = -29.74 + 360 ≈ 330.26 degreesRound to Nearest Hundredth: Round the direction angle to the nearest hundredth. θ ≈ 330.26^(@)

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vec(u)=(7,-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=◻^(@)

$\vec{u}=(7,-4)$ $\newline$ Find the direction angle of $\newline$ $\vec{u}$ . Enter your answer as an angle in degrees between $\newline$ $0^{\circ}$ and $\newline$ $360^{\circ}$ 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}=(7,-4)

\newline

Find the direction angle of

\newline

\vec{u}

. Enter your answer as an angle in degrees between

\newline

0^{\circ}

and

\newline

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=\square^{\circ}

Identify Components and Formula: Identify the components of the vector $u$ and the formula to find the direction angle. Vector $u$ has components $u = (7, -4)$ . The direction angle $\theta$ of a vector can be found using the arctangent function, where $\theta = \text{arctan}(y/x)$ for a vector with components $(x, y)$ .
Calculate Arctangent: Calculate the arctangent of the y-component divided by the x-component to find the direction angle in radians. $\newline$ $\theta = \arctan(\frac{-4}{7})$
Use Calculator for Value: Use a calculator to find the arctangent value. $\theta = \arctan\left(\frac{-4}{7}\right) \approx -29.74$ degrees (in radians, this would be approximately $-0.5191$ radians)
Adjust for Quadrant: Since the vector is in the fourth quadrant ( $x$ is positive and $y$ is negative), we need to add $360$ degrees to the angle to find the direction angle between $0$ and $360$ degrees. $\newline$ $\theta = -29.74 + 360 \approx 330.26$ degrees
Round to Nearest Hundredth: Round the direction angle to the nearest hundredth. $\theta \approx 330.26^\circ$