vec(u)=(4,-2) 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. To find this angle, we use the arctangent function (tan^(-1)), which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector. Calculation: theta = tan^(-1)(y/x) = tan^(-1)(-2/4) = tan^(-1)(-0.5).Calculation of theta: Using a calculator to find the arctangent of -0.5, we get an initial angle. However, since the vector is in the fourth quadrant (because the x-coordinate is positive and the y-coordinate is negative), we need to add 360 degrees to the initial angle if it's negative to ensure the angle is between 0 and 360 degrees. Calculation: Initial angle = tan^(-1)(-0.5) ≈ -26.57 degrees. Since it's negative, we add 360 degrees to find the direction angle in the correct range. Theta = -26.57 + 360 ≈ 333.43 degrees.

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vec(u)=(4,-2)
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=◻" 。 "

$\vec{u}=(4,-2)$ $\newline$ 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

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\vec{u}=(4,-2)

\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. To find this angle, we use the arctangent function ( $\tan^{-1}$ ), which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector. $\newline$ Calculation: $\theta = \tan^{-1}(\frac{y}{x}) = \tan^{-1}(\frac{-2}{4}) = \tan^{-1}(-0.5)$ .
Calculation of theta: Using a calculator to find the arctangent of $-0.5$ , we get an initial angle. However, since the vector is in the fourth quadrant (because the $x$ -coordinate is positive and the $y$ -coordinate is negative), we need to add $360$ degrees to the initial angle if it's negative to ensure the angle is between $0$ and $360$ degrees. $\newline$ Calculation: Initial angle = $\tan^{-1}(-0.5) \approx -26.57$ degrees. Since it's negative, we add $360$ degrees to find the direction angle in the correct range. $\newline$ Theta = $-26.57 + 360 \approx 333.43$ degrees.