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vec(u)=(6,7) 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=(6,7) \vec{u}=(6,7) \newlineFind the direction angle of u⃗ \vec{u} .\newlineEnter your answer as an angle in degrees between 0∘ 0^{\circ} and 360∘ 360^{\circ} rounded to the nearest hundredth.\newlineθ= \theta= \newline□ \square

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Full solution

Q. u⃗=(6,7) \vec{u}=(6,7) \newlineFind the direction angle of u⃗ \vec{u} .\newlineEnter your answer as an angle in degrees between 0∘ 0^{\circ} and 360∘ 360^{\circ} rounded to the nearest hundredth.\newlineθ= \theta= \newline□ \square
  1. Calculate direction angle: Calculate the direction angle using the arctangent function. θ=arctan⁡(76)\theta = \arctan(\frac{7}{6})
  2. Use calculator for arctan: Use a calculator to find the value of arctan(76)\text{arctan}\left(\frac{7}{6}\right).θ≈arctan(1.1667)\theta \approx \text{arctan}(1.1667)
  3. Round result to nearest hundredth: Round the result to the nearest hundredth. θ≈49.40\theta \approx 49.40 degrees

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