vec(u)=(-4,-3) 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)=(-4,-3) 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 Slope: To find the direction angle of the vector vec(u) = (-4, -3), we need to calculate the angle that this vector makes with the positive x-axis. The direction angle, often denoted as θ, can be found using the arctangent function (tan^(-1)) of the slope of the vector, which is the ratio of its y-component to its x-component. The formula to find the direction angle is θ = tan^(-1)(y/x).Use Arctangent Function: First, we calculate the slope of the vector by dividing its y-component by its x-component. For vec(u) = (-4, -3), the slope is (-3)/(-4) = 3/4.Adjust for Quadrant: Next, we use the arctangent function to find the angle that corresponds to this slope. However, since the vector is in the third quadrant (both x and y components are negative), the angle given by the arctangent function will be in the fourth quadrant. We need to add 180° to this angle to get the correct direction angle in the third quadrant. θ = tan^(-1)(3/4) + 180°Calculate Arctangent: Now, we calculate the arctangent of 3/4 using a calculator. θ = tan^(-1)(3/4) ≈ 36.87°Add 180°: Finally, we add 180° to the angle we found to get the direction angle in the correct quadrant. θ = 36.87° + 180° θ ≈ 216.87°

$\vec{u}=(-4,-3)$ $\newline$ 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=(−4,−3) \vec{u}=(-4,-3) u=(−4,−3)\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=□∘

$\vec{u}=(-4,-3)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$