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=◻" 。 "

Definition of Direction Angle: The direction angle of a vector in the coordinate plane is the angle the vector makes with the positive x-axis. The direction angle, often denoted as θ, can be found using the arctangent function (also known as the inverse tangent or atan), which is the ratio of the y-coordinate to the x-coordinate of the vector.Identifying Vector Components: First, we identify the x and y components of the vector vec(u) = (2,5). Here, x = 2 and y = 5.Calculating Direction Angle: Next, we calculate the direction angle using the arctangent function: θ = atan(y/x) = atan(5/2).Using Arctangent Function: Using a calculator, we find the arctangent of 5/2: θ ≈ atan(2.5) ≈ 68.19859 degrees.Rounding to Nearest Hundredth: Since the vector is in the first quadrant (where both x and y are positive), the direction angle θ is already between 0° and 90°. Therefore, we do not need to adjust the angle, and we can round it to the nearest hundredth: θ ≈ 68.20°.

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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=◻" 。 "

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

Inverses of sin, cos, and tan: degrees

Full solution

\vec{u}=(2,5)

\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}

Definition of Direction Angle: The direction angle of a vector in the coordinate plane is the angle the vector makes with the positive x-axis. The direction angle, often denoted as $\theta$ , can be found using the arctangent function (also known as the inverse tangent or $\text{atan}$ ), which is the ratio of the y-coordinate to the x-coordinate of the vector.
Identifying Vector Components: First, we identify the $x$ and $y$ components of the vector $\vec{u} = (2,5)$ . Here, $x = 2$ and $y = 5$ .
Calculating Direction Angle: Next, we calculate the direction angle using the arctangent function: $\theta = \text{atan}(y/x) = \text{atan}(5/2)$ .
Using Arctangent Function: Using a calculator, we find the arctangent of $\frac{5}{2}$ : $\theta \approx \text{atan}(2.5) \approx 68.19859$ degrees.
Rounding to Nearest Hundredth: Since the vector is in the first quadrant (where both $x$ and $y$ are positive), the direction angle $\theta$ is already between $0^\circ$ and $90^\circ$ . Therefore, we do not need to adjust the angle, and we can round it to the nearest hundredth: $\newline$ $\theta \approx 68.20^\circ$ .