vec(u)=(-7,-10) 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)=(-7,-10) 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 direction angle: To find the direction angle of the vector vec(u) = (-7, -10), 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.Find tangent of angle: First, we calculate the tangent of the angle θ using the y-coordinate and the x-coordinate of the vector vec(u). The tangent of θ is given by tan(θ) = y/x. For vec(u) = (-7, -10), this is tan(θ) = -10 / -7.Take arctangent: Performing the division, we get tan(θ) = 10/7. Now we need to take the arctangent of this value to find the angle θ in radians. However, since we want the angle in degrees and between 0° and 360°, we will need to adjust the angle we get from the arctangent function accordingly.Convert to degrees: Using a calculator, we find the arctangent of 10/7, which gives us θ in radians. To convert this to degrees, we multiply by 180/π. The calculator will give us an angle in the first quadrant, but since the vector has negative x and y components, the actual direction angle is in the third quadrant.Adjust for quadrant: The angle from the arctangent function is approximately atan(10/7) ≈ 55.00°. Since the vector is in the third quadrant, we add 180° to this angle to find the correct direction angle θ.Final direction angle: Adding 180° to 55.00° gives us θ ≈ 235.00°. This is the direction angle of the vector vec(u) in the third quadrant, which is between 0° and 360°.

$\vec{u}=(-7,-10)$ $\newline$ 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=(−7,−10) \vec{u}=(-7,-10) u=(−7,−10)\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=□∘

$\vec{u}=(-7,-10)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$