vec(u)=(7,-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)=(7,-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 ratio of coordinates: To find the direction angle of the vector vec(u) = (7, -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 (also known as the inverse tangent or atan), 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 ratio of the y-coordinate to the x-coordinate of the vector vec(u). This ratio is -4/7. We will use this ratio to find the angle with the arctangent function.Adjust angle for quadrant: Next, we use the arctangent function to find the angle θ. We have to be careful because the arctangent function will give us an angle in the range of -90° to 90°, but we want the angle in the range of 0° to 360°. Since the x-coordinate is positive and the y-coordinate is negative, the vector is in the fourth quadrant. θ = atan(-4/7)Calculate direction angle: Using a calculator, we find that θ ≈ atan(-4/7) ≈ -29.74°. However, this is the angle measured counterclockwise from the positive x-axis to the vector, and since it's negative, it's actually measured clockwise. To find the direction angle in the range of 0° to 360°, we add 360° to this angle. θ = 360° - 29.74°Add 360° for range adjustment: Performing the calculation gives us the direction angle of the vector in the correct range: θ = 360° - 29.74° ≈ 330.26°

$\vec{u}=(7,-4)$ $\newline$ 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=(7,−4) \vec{u}=(7,-4) u=(7,−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=□∘

$\vec{u}=(7,-4)$ $\newline$ 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. $\newline$ $\theta= \square^{\circ}$