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=◻" 。 "

Question

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=◻" 。 "

Bytelearn · Accepted Answer

Use Arctangent Function: To find the direction angle of the vector $ \vec{u} = (-2,5) $, 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 for the direction angle $ \theta $ is: $$ \theta = \arctan\left(\frac{y}{x}\right) $$ where $ x $ and $ y $ are the x-coordinate and y-coordinate of the vector, respectively.Plug Coordinates into Formula: First, we plug the coordinates of $ \vec{u} $ into the formula: $$ \theta = \arctan\left(\frac{5}{-2}\right) $$Calculate Arctangent: Calculating the arctangent of $ \frac{5}{-2} $ gives us an angle in radians. We need to convert this angle to degrees and make sure it is in the range of 0° to 360°. Since the vector is in the second quadrant (negative x-coordinate and positive y-coordinate), the direction angle $ \theta $ will be $ 180° $ minus the angle we find.Convert to Degrees: Using a calculator, we find that: $$ \theta = \arctan\left(\frac{5}{-2}\right) \approx \arctan(-2.5) $$ $$ \theta \approx -68.1985905° $$ Since the angle is negative, we add 180° to find the direction angle in the second quadrant: $$ \theta = 180° - (-68.1985905°) $$ $$ \theta = 180° + 68.1985905° $$ $$ \theta \approx 248.1985905° $$Round to Nearest Hundredth: Finally, we round the direction angle to the nearest hundredth: $$ \theta \approx 248.20° $$

$\vec{u}=(-2,5)$ $\newline$ 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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More problems from Inverses of sin, cos, and tan: degrees

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u⃗=(−2,5) \vec{u}=(-2,5) u=(−2,5)\newlineFind the direction angle of u⃗ \vec{u} u. Enter your answer as an angle in degrees between 0∘ 0^{\circ} 0∘ and 360∘ 360^{\circ} 360∘ rounded to the nearest hundredth.\newlineθ=□∘ \theta=\square^{\circ} θ=□∘

$\vec{u}=(-2,5)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$