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vec(u)=(5,3)
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=◻" 。 "

$\vec{u}=(5,3)$ $\newline$ Find the direction angle of $\vec{u}$ . 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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Inverses of sin, cos, and tan: degrees

Full solution

Q.

\vec{u}=(5,3)

\newline

Find the direction angle of

\vec{u}

. Enter your answer as an angle in degrees between

0^{\circ}

and

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=\square^{\circ}

Step $1$ : Formula for direction angle: To find the direction angle of the vector $\vec{u} = (5,3)$ , we need to use the arctangent function, which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector. The formula to find the direction angle $\theta$ is: $\newline$ $\theta = \arctan(\frac{y}{x})$ $\newline$ where $x$ and $y$ are the x-coordinate and y-coordinate of the vector, respectively.
Step $2$ : Plugging in the coordinates: Now we will plug in the values of the coordinates of $\vec{u}$ into the formula: $\theta = \arctan(\frac{3}{5})$
Step $3$ : Calculating the arctangent: Using a calculator, we find the arctangent of $\frac{3}{5}$ : $\newline$ $\theta \approx \arctan(0.6)$ $\newline$ $\theta \approx 30.96$ degrees
Step $4$ : Determining the direction angle: Since the vector $\vec{u}$ is in the first quadrant (both $x$ and $y$ are positive), the direction angle $\theta$ is already between $0^\circ$ and $360^\circ$ . Therefore, we do not need to adjust the angle further.

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