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vec(u)=(8,6) 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=◻" 。 "

u⃗=(8,6) \vec{u}=(8,6) \newlineFind the direction angle of u⃗ \vec{u} . Enter your answer as an angle in degrees between 0∘ 0^{\circ} and 360∘ 360^{\circ} rounded to the nearest hundredth.\newlineθ=□∘ \theta= \square^{\circ}

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Inverses of sin, cos, and tan: degreesright chevron icon

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Q. u⃗=(8,6) \vec{u}=(8,6) \newlineFind the direction angle of u⃗ \vec{u} . Enter your answer as an angle in degrees between 0∘ 0^{\circ} and 360∘ 360^{\circ} rounded to the nearest hundredth.\newlineθ=□∘ \theta= \square^{\circ}
  1. Calculate Tangent Ratio: To find the direction angle of the vector u⃗=(8,6) \vec{u} = (8,6) , we need to calculate the angle θ \theta that the vector makes with the positive x-axis. The direction angle can be found using the arctangent function, which is the inverse of the tangent function. The tangent of the angle is the ratio of the y-coordinate to the x-coordinate of the vector. So, we calculate tan⁡(θ)=yx \tan(\theta) = \frac{y}{x} .
  2. Substitute Values: Substitute the values of the vector u⃗=(8,6) \vec{u} = (8,6) into the formula to get tan⁡(θ)=68=34 \tan(\theta) = \frac{6}{8} = \frac{3}{4} .
  3. Use Arctangent Function: Now, we use the arctangent function to find the angle θ \theta . We calculate θ=arctan⁡(34) \theta = \arctan\left(\frac{3}{4}\right) . This will give us the angle in radians, which we then convert to degrees.
  4. Convert to Degrees: Using a calculator, we find that θ≈arctan⁡(34) \theta \approx \arctan\left(\frac{3}{4}\right) in degrees is approximately 3636.8787 degrees.
  5. Check Quadrant: Since the vector u⃗=(8,6) \vec{u} = (8,6) is in the first quadrant (both x and y are positive), the direction angle θ \theta is already between 00 and 9090 degrees. Therefore, we do not need to adjust the angle further.

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