vec(u)=(8,-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)=(8,-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

Finding the Direction Angle: To find the direction angle of the vector vec(u) = (8, -3), we need to calculate the angle θ that the vector makes with the positive x-axis. The direction angle can be found using the arctangent function (tan^(-1)), which gives us the angle in radians. We can then convert this angle to degrees. The formula to find the angle is θ = tan^(-1)(y/x), where x and y are the components of the vector.Plugging in the Components: First, we plug the components of vec(u) into the formula: θ = tan^(-1)(-3/8). This will give us the angle in radians.Calculating the Angle in Radians: Using a calculator, we find that θ = tan^(-1)(-3/8) ≈ -20.556 degrees. However, this angle is not between 0° and 360°, so we need to adjust it.Converting the Angle to Degrees: Since the vector is in the fourth quadrant (because x is positive and y is negative), we add 360° to the angle to find the direction angle in the specified range. Therefore, the direction angle is -20.556 degrees + 360 degrees = 339.444 degrees.Adjusting the Angle: We round the direction angle to the nearest hundredth, which gives us θ ≈ 339.44°.

$\vec{u}=(8,-3)$ $\newline$ 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=(8,−3) \vec{u}=(8,-3) u=(8,−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=□∘

$\vec{u}=(8,-3)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$