vec(u)=(-10,7) 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)=(-10,7) 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) = (-10,7), we need to calculate the angle that the 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.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 = 7/(-10) = -0.7.Determine Quadrant: Next, we use the arctangent function to find the angle θ whose tangent is -0.7. We must be careful to place the angle in the correct quadrant. Since the x-coordinate is negative and the y-coordinate is positive, vec(u) lies in the second quadrant, where the direction angles are between 90° and 180°. θ = atan(-0.7).Calculate Direction Angle: Using a calculator, we find that: θ = atan(-0.7) ≈ -35.00°. However, this angle is measured from the positive x-axis in the clockwise direction. To find the direction angle between 0° and 360°, we add 180° to this angle because it is in the second quadrant. θ = -35.00° + 180° = 145.00°.Round to Nearest Hundredth: We round the direction angle to the nearest hundredth as requested: θ ≈ 145.00°.

$\vec{u}=(-10,7)$ $\newline$ 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=(−10,7) \vec{u}=(-10,7) u=(−10,7)\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=□∘

$\vec{u}=(-10,7)$ $\newline$ 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. $\newline$ $\theta=\square^{\circ}$