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=◻^(@)

Identify Formula: Identify the formula for the direction angle of a vector. The direction angle theta of a vector vec(u)=(x,y) can be found using the arctangent function: theta = arctan(y/x). However, since arctan only gives values from -90 to 90 degrees, we need to adjust the angle based on the quadrant in which the vector lies.Calculate Arctangent: Calculate the arctangent of the y-coordinate divided by the x-coordinate. For vec(u)=(-10,7), we have x=-10 and y=7. Thus, theta = arctan(7/(-10)) = arctan(-0.7). Using a calculator, we find that arctan(-0.7) ≈ -35.54 degrees.Adjust Based on Quadrant: Adjust the angle based on the quadrant. Since the x-coordinate is negative and the y-coordinate is positive, vec(u) lies in the second quadrant. In the second quadrant, we must add 180 degrees to the arctangent value to find the correct direction angle.Add 180 Degrees: Add 180 degrees to the arctangent value. theta = -35.54 degrees + 180 degrees = 144.46 degrees.Round to Nearest Hundredth: Round the direction angle to the nearest hundredth. theta ≈ 144.46 degrees (rounded to the nearest hundredth).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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=◻^(@)

$\vec{u} = (-10,7)$ $\newline$ Find the direction angle of $\vec{u}$ . Enter your answer as an angle in degrees between $\newline$ $0^{\circ}$ and $360^{\circ}$ rounded to the nearest hundredth. $\newline$ $\theta=\square^{\circ}$

View step-by-step help

Home

Math Problems

Algebra 2

Find Coordinate on Unit Circle

Full solution

\vec{u} = (-10,7)

\newline

Find the direction angle of

\vec{u}

. Enter your answer as an angle in degrees between

\newline

0^{\circ}

and

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=\square^{\circ}

Identify Formula: Identify the formula for the direction angle of a vector. $\newline$ The direction angle $\theta$ of a vector $\vec{u}=(x,y)$ can be found using the arctangent function: $\theta = \text{arctan}(y/x)$ . However, since $\text{arctan}$ only gives values from $-90$ to $90$ degrees, we need to adjust the angle based on the quadrant in which the vector lies.
Calculate Arctangent: Calculate the arctangent of the y-coordinate divided by the x-coordinate. $\newline$ For $\vec{u}=(-10,7)$ , we have $x=-10$ and $y=7$ . Thus, $\theta = \arctan\left(\frac{7}{-10}\right) = \arctan(-0.7)$ . $\newline$ Using a calculator, we find that $\arctan(-0.7) \approx -35.54$ degrees.
Adjust Based on Quadrant: Adjust the angle based on the quadrant. $\newline$ Since the x-coordinate is negative and the y-coordinate is positive, $\vec{u}$ lies in the second quadrant. In the second quadrant, we must add $180$ degrees to the arctangent value to find the correct direction angle.
Add $180$ Degrees: Add $180$ degrees to the arctangent value. $\newline$ $\theta = -35.54$ degrees $+ 180$ degrees $= 144.46$ degrees.
Round to Nearest Hundredth: Round the direction angle to the nearest hundredth. $\newline$ $\theta \approx 144.46$ degrees (rounded to the nearest hundredth).