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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} . 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

Full solution

Q. u⃗=(6,7) \vec{u}=(6,7) \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 direction angle: Calculate the direction angle using the arctangent function. θ=arctan⁡(76)\theta = \arctan(\frac{7}{6})
  2. Use calculator for theta: Use a calculator to find the value of θ\theta.θ≈arctan⁡(1.1667)\theta \approx \arctan(1.1667)θ≈49.3987\theta \approx 49.3987 degrees
  3. Round θ\theta to nearest: Round θ\theta to the nearest hundredth.θ≈49.40\theta \approx 49.40 degrees

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