vec(u)=(-5,-8) 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)=(-5,-8) 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 Tangent Ratio: To find the direction angle of the vector vec(u) = (-5, -8), 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) or atan), which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector.Use Arctangent Function: First, we calculate the tangent of the angle θ using the coordinates of vec(u). The tangent of θ is the ratio of the y-coordinate to the x-coordinate. tan(θ) = y / x = -8 / -5 = 8 / 5Add 180 Degrees: Next, we use the arctangent function to find the angle θ whose tangent is 8/5. However, since the vector is in the third quadrant (both x and y are negative), we need to add 180° to the angle we get from the arctangent function to find the correct direction angle that is between 0° and 360°. θ = atan(8/5) + 180°Calculate Arctangent: We calculate the arctangent of 8/5 using a calculator and then add 180° to find the direction angle. θ ≈ atan(8/5) + 180° ≈ 58.00° + 180° ≈ 238.00°Round to Nearest Hundredth: Finally, we round the direction angle to the nearest hundredth as requested. θ ≈ 238.00°

$\vec{u}=(-5,-8)$ $\newline$ 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=(−5,−8) \vec{u}=(-5,-8) u=(−5,−8)\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=□∘

$\vec{u}=(-5,-8)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$