vec(u)=(-1,4) 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)=(-1,4) 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: To find the direction angle of the vector vec(u) = (-1,4), 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) or atan), which gives us the angle whose tangent is the ratio of the y-coordinate to the x-coordinate of the vector.Consider Quadrant: 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 = 4/(-1) = -4Use Arctangent Function: Next, we use the arctangent function to find the angle θ whose tangent is -4. However, we must be careful with the signs and the quadrant in which the vector lies. Since the x-coordinate is negative and the y-coordinate is positive, vec(u) lies in the second quadrant. The arctangent function will give us an angle in the fourth quadrant, so we need to add 180° to get the angle in the second quadrant. θ = atan(-4) + 180°Add 180°: We calculate the arctangent of -4 using a calculator and then add 180° to find the direction angle in the second quadrant. θ ≈ atan(-4) + 180° ≈ -75.96° + 180° ≈ 104.04°Round to Nearest Hundredth: We round the direction angle to the nearest hundredth as requested. θ ≈ 104.04° (rounded to the nearest hundredth)

$\vec{u}=(-1,4)$ $\newline$ 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

Related topics

u⃗=(−1,4) \vec{u}=(-1,4) u=(−1,4)\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=□∘

$\vec{u}=(-1,4)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$