vec(u)=(-8,-9) 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)=(-8,-9) 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

Find direction angle of vector: To find the direction angle of the vector $ \vec{u} = (-8, -9) $, we need to calculate the angle that this vector makes with the positive x-axis. The direction angle $ \theta $ 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.Calculate arctangent of ratio: First, we calculate the arctangent of the ratio of the y-coordinate to the x-coordinate of the vector $ \vec{u} $. Since $ \vec{u} = (-8, -9) $, we have: $ \theta = \arctan\left(\frac{-9}{-8}\right) $.Use calculator to find arctan: Using a calculator, we find that: $ \theta = \arctan\left(\frac{-9}{-8}\right) \approx \arctan(1.125) $.Adjust angle for correct quadrant: The arctan of 1.125 gives us an angle in the first quadrant, but since both the x and y components of the vector are negative, the vector is actually in the third quadrant. We need to add 180° to the angle we get from the arctan function to place it in the correct quadrant.Calculate final angle: Calculating the angle, we get: $ \theta \approx \arctan(1.125) + 180° $.Round angle to nearest hundredth: Using a calculator, we find that: $ \theta \approx 48.37° + 180° $.Adding 180° to 48.37°, we get: $ \theta \approx 228.37° $.We round the angle to the nearest hundredth, as requested: $ \theta \approx 228.37° $.

$\vec{u}=(-8,-9)$ $\newline$ 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=(−8,−9) \vec{u}=(-8,-9) u=(−8,−9)\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=□∘

$\vec{u}=(-8,-9)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$