vec(u)=(-9,3) 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= ◻^(@)

Calculate tangent: To find the direction angle of vec(u), we need to use the arctangent function, which gives us the angle whose tangent is the quotient of the y-coordinate and the x-coordinate of the vector.Find arctangent: First, let's calculate the tangent of the direction angle, which is the y-coordinate divided by the x-coordinate of vec(u). So, tan(theta) = 3 / (-9).Calculate angle: Now, we calculate tan(theta) = 3 / (-9) = -1/3.Adjust for quadrant: Next, we use the arctangent function to find the angle. So, theta = arctan(-1/3). We'll use a calculator for this.After using the calculator, we find that theta ≈ arctan(-1/3) ≈ -18.43°.However, we want the direction angle to be between 0° and 360°. Since our vector is in the second quadrant (negative x and positive y), we add 180° to the angle we found.So, theta = -18.43° + 180° = 161.57°.

Home

Math Problems

Algebra 2

Find trigonometric functions using a calculator

Full solution

\vec{u} = (-9,3)

\newline

Find the direction angle of

\vec{u}

\newline

Enter your answer as an angle in degrees between

0^{\circ}

and

360^{\circ}

rounded to the nearest hundredth.

\newline

\theta=

\square^{\circ}

Calculate tangent: To find the direction angle of $\vec{u}$ , we need to use the arctangent function, which gives us the angle whose tangent is the quotient of the y-coordinate and the x-coordinate of the vector.
Find arctangent: First, let's calculate the tangent of the direction angle, which is the y-coordinate divided by the x-coordinate of $\vec{u}$ . So, $\tan(\theta) = \frac{3}{-9}$ .
Calculate angle: Now, we calculate $\tan(\theta) = \frac{3}{(-9)} = -\frac{1}{3}$ .
Adjust for quadrant: Next, we use the arctangent function to find the angle. So, $\theta = \text{arctan}(-\frac{1}{3})$ . We'll use a calculator for this.
Adjust for quadrant: Next, we use the arctangent function to find the angle. So, $\theta = \text{arctan}(-\frac{1}{3})$ . We'll use a calculator for this.After using the calculator, we find that $\theta \approx \text{arctan}(-\frac{1}{3}) \approx -18.43^\circ$ .
Adjust for quadrant: Next, we use the arctangent function to find the angle. So, $\theta = \text{arctan}(-\frac{1}{3})$ . We'll use a calculator for this.After using the calculator, we find that $\theta \approx \text{arctan}(-\frac{1}{3}) \approx -18.43^\circ$ .However, we want the direction angle to be between $0^\circ$ and $360^\circ$ . Since our vector is in the second quadrant (negative $x$ and positive $y$ ), we add $180^\circ$ to the angle we found.
Adjust for quadrant: Next, we use the arctangent function to find the angle. So, $\theta = \text{arctan}(-\frac{1}{3})$ . We'll use a calculator for this.After using the calculator, we find that $\theta \approx \text{arctan}(-\frac{1}{3}) \approx -18.43^\circ$ .However, we want the direction angle to be between $0^\circ$ and $360^\circ$ . Since our vector is in the second quadrant (negative x and positive y), we add $180^\circ$ to the angle we found.So, $\theta = -18.43^\circ + 180^\circ = 161.57^\circ$ .