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=◻^(@)

Question

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=◻^(@)

Bytelearn · Accepted Answer

Calculate Tangent Ratio: To find the direction angle of the vector $ \vec{u} = (6,7) $, we need to calculate the angle $ \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.Find Arctangent: First, we calculate the tangent of the angle $ \theta $ using the coordinates of the vector $ \vec{u} $: $$ \tan(\theta) = \frac{y}{x} = \frac{7}{6} $$Calculate Angle in Degrees: Next, we find the angle $ \theta $ by taking the arctangent of $ \frac{7}{6} $: $$ \theta = \arctan\left(\frac{7}{6}\right) $$ We will use a calculator to find the value of $ \theta $ in degrees.Check Quadrant: Using a calculator, we find that: $$ \theta \approx \arctan\left(\frac{7}{6}\right) \approx 49.3987 \text{ degrees} $$Round to Nearest Hundredth: Since the vector $ \vec{u} $ is in the first quadrant (both x and y are positive), the direction angle $ \theta $ is already between 0 and 360 degrees. Therefore, we do not need to adjust the angle further.Finally, we round the angle to the nearest hundredth as requested: $$ \theta \approx 49.40^{\circ} $$

$\vec{u}=(6,7)$ $\newline$ Find the direction angle of $\newline$ $\vec{u}$ . Enter your answer as an angle in degrees between $\newline$ $0^{\circ}$ and $\newline$ $360^{\circ}$ rounded to the nearest hundredth. $\newline$ $\theta=\square^{\circ}$

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More problems from Inverses of trigonometric functions using a calculator

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u⃗=(6,7)\vec{u}=(6,7)u=(6,7)\newlineFind the direction angle of \newlineu⃗\vec{u}u. Enter your answer as an angle in degrees between \newline0∘0^{\circ}0∘ and \newline360∘360^{\circ}360∘ rounded to the nearest hundredth.\newlineθ=□∘\theta=\square^{\circ}θ=□∘

$\vec{u}=(6,7)$ $\newline$ Find the direction angle of $\newline$ $\vec{u}$ . Enter your answer as an angle in degrees between $\newline$ $0^{\circ}$ and $\newline$ $360^{\circ}$ rounded to the nearest hundredth. $\newline$ $\theta=\square^{\circ}$