vec(u)=(6,-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)=(6,-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

Calculate Tangent Ratio: To find the direction angle of the vector vec(u) = (6, -8), we need to calculate the angle that this vector makes with the positive x-axis. The direction angle, often denoted as θ, can be found using the arctangent function (tan^(-1)) which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector.Use Arctangent Function: First, we calculate the tangent of the angle θ using the coordinates of vec(u). The tangent of θ is the ratio of the y-coordinate to the x-coordinate. tan(θ) = y/x = -8/6 = -4/3.Determine Quadrant: Next, we use the arctangent function to find the angle θ whose tangent is -4/3. We must be careful to place the angle in the correct quadrant. Since the x-coordinate is positive and the y-coordinate is negative, vec(u) is in the fourth quadrant where the direction angles are between 270° and 360°. θ = arctan(-4/3).Adjust for Quadrant: Using a calculator, we find the arctangent of -4/3. However, this will give us an angle in the second quadrant, so we must add 360° to get the angle in the fourth quadrant. θ = arctan(-4/3) + 360°.Final Calculation: After calculating, we get: θ ≈ arctan(-4/3) + 360° ≈ -53.13° + 360° ≈ 306.87°. We round this to the nearest hundredth as requested.

$\vec{u}=(6,-8)$ $\newline$ 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=(6,−8) \vec{u}=(6,-8) u=(6,−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=□∘

$\vec{u}=(6,-8)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$