The components of vector A⃗ are Ax = + 3.90 and Ay = -4.00. What is the angle measured counterclockwise from the +x-axis to vector A⃗ ?

Ah, let me dust off my protractor and calculate that for you! Since we have Ax = +3.90 and Ay = -4.00, we can use some math magic to find the angle. We can start by calculating the magnitude of vector A⃗ using the Pythagorean theorem:

|A⃗ | = sqrt(Ax^2 + Ay^2)
= sqrt((3.9)^2 + (-4)^2)
= sqrt(15.21 + 16)
= sqrt(31.21)
≈ 5.59

Now, to find the angle, we can use the inverse tangent (tan⁻¹) function:

θ = tan⁻¹(Ay/Ax)
= tan⁻¹((-4)/(3.9))
≈ -48.26 degrees

So, the angle measured counterclockwise from the +x-axis to vector A⃗ is approximately -48.26 degrees. Just remember, in the world of vectors and angles, clockwise is the wrong way to go!

To find the angle measured counterclockwise from the +x-axis to vector A⃗, we can use trigonometry.

First, let's calculate the magnitude of vector A⃗ using the Pythagorean theorem:

Magnitude of vector A⃗ (|A⃗|) = sqrt((Ax)^2 + (Ay)^2)
= sqrt((3.90)^2 + (-4.00)^2)
≈ 5.22

Next, let's calculate the angle using the inverse tangent function:

Angle = arctan(Ay / Ax)
= arctan((-4.00) / 3.90)
≈ -46.11°

The angle is approximately -46.11° counterclockwise from the +x-axis.

To find the angle measured counterclockwise from the +x-axis to vector A⃗, we can use the inverse tangent function. The inverse tangent, often denoted as tan⁻¹ or atan, is the function that gives the angle whose tangent is a given number.

First, we need to calculate the tangent of the angle. The tangent of an angle can be found using the formula:

tan(θ) = opposite/adjacent

In this case, the opposite side is Ay = -4.00 and the adjacent side is Ax = +3.90.

So, we have:

tan(θ) = (-4.00) / (3.90)

Using a calculator or software that has a tangent function (tan), we can find the value of θ:

θ = tan⁻¹((-4.00) / (3.90))

Evaluate this expression using a calculator or software, and you will find the angle in radians. To convert radians to degrees, simply multiply the result by (180/π).

Note: Make sure your calculator or software is set to the correct angle mode (either degrees or radians) before performing the calculation.

Tan A = Y/X = -4.0/3.90 = -1.02564.

A = -45.7o = 45.7o CW from +x-axis. = 314.3o CCW from +x-axis.