vec(u)=(5,8) 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)=(5,8) 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

Use Arctangent Function: To find the direction angle of the vector vec(u) = (5,8), we need to use the arctangent function, which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector. The formula for the direction angle θ is θ = arctan(y/x), where y is the y-coordinate and x is the x-coordinate of the vector.Calculate Ratio: First, we calculate the ratio of the y-coordinate to the x-coordinate of the vector vec(u) = (5,8). This ratio is 8/5.Find Angle: Next, we use the arctangent function to find the angle. θ = arctan(8/5). We need to ensure that our calculator is set to degree mode since we want the answer in degrees.Calculate Arctangent: After calculating the arctangent of 8/5, we get θ ≈ arctan(1.6). Using a calculator, we find that θ ≈ 58.00 degrees. This is the direction angle of the vector in the first quadrant, which is between 0° and 90°.Check Quadrant: Since the vector vec(u) = (5,8) is in the first quadrant and we are looking for an angle between 0° and 360°, the direction angle we found is already in the correct range. Therefore, we do not need to adjust the angle.

$\vec{u}=(5,8)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$

Full solution

More problems from Inverses of sin, cos, and tan: degrees

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u⃗=(5,8) \vec{u}=(5,8) u=(5,8)\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=□∘

$\vec{u}=(5,8)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$