vec(u)=(9,-6) 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)=(9,-6) 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

Calculate Ratio: To find the direction angle of the vector $ \vec{u} = (9, -6) $, we need to calculate the angle that the vector makes with the positive x-axis. The direction angle $ \theta $ can be found using the arctangent function, which is the inverse of the tangent function. The tangent of the angle is the ratio of the y-coordinate to the x-coordinate of the vector. However, since the y-coordinate is negative and the x-coordinate is positive, the vector lies in the fourth quadrant, and we must add 360 degrees to the arctangent of the ratio to get the angle in the range [0, 360) degrees.Find Arctangent: First, calculate the ratio of the y-coordinate to the x-coordinate of the vector $ \vec{u} $: $ \tan(\theta) = \frac{-6}{9} = \frac{-2}{3} $.Calculate Angle: Next, use the arctangent function to find the angle $ \theta $ that corresponds to this ratio. Remember that the arctangent function will give us an angle in the range $(-90^{\circ}, 90^{\circ})$, so we need to adjust it for the fourth quadrant. $ \theta = \arctan\left(\frac{-2}{3}\right) $.Adjust for Quadrant: Using a calculator, we find that: $ \theta \approx \arctan\left(\frac{-2}{3}\right) \approx -33.69^{\circ} $. Since this angle is in the fourth quadrant, we add 360 degrees to get the direction angle in the range [0, 360) degrees. $ \theta = -33.69^{\circ} + 360^{\circ} $.Find Final Angle: Perform the addition to find the final direction angle: $ \theta \approx -33.69^{\circ} + 360^{\circ} \approx 326.31^{\circ} $.

$\vec{u}=(9,-6)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$

Full solution

More problems from Inverses of sin, cos, and tan: degrees

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u⃗=(9,−6) \vec{u}=(9,-6) u=(9,−6)\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=□∘

$\vec{u}=(9,-6)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$