vec(u)=(-9,3) 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)=(-9,3) 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

Use Arctangent Function: To find the direction angle of the vector vec(u) with components (-9,3), we need to use the arctangent function, which gives us the angle whose tangent is the ratio of the y-component to the x-component of the vector. The formula for the direction angle theta is theta = arctan(y/x). However, since the vector is in the second quadrant (x is negative and y is positive), we need to add 180 degrees to the angle we get from the arctangent function to get the correct direction angle.Calculate Arctangent: First, calculate the arctangent of the ratio of the y-component to the x-component of the vector vec(u). The y-component is 3 and the x-component is -9. So, arctan(3/-9) = arctan(-1/3).Find Correct Angle: Using a calculator, we find that arctan(-1/3) is approximately -18.43 degrees. Since the arctangent function can return values between -90 and 90 degrees, and our vector is in the second quadrant, we need to add 180 degrees to this value to find the correct direction angle.Add 180 Degrees: Adding 180 degrees to -18.43 degrees gives us 161.57 degrees. This is the direction angle of the vector vec(u) in the range of 0 to 360 degrees.

$\vec{u}=(-9,3)$ $\newline$ 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=(−9,3) \vec{u}=(-9,3) u=(−9,3)\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=□∘

$\vec{u}=(-9,3)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$