The x component of a certain vector is -86.0 units and the y component is +75.0 units.
The magnitude of the vector is 114 m.
What is the angle between the direction of the vector and the positive direction of x? Use the convention that positive angles are measured counterclockwise from the +x axis and negative angles are measured clockwise from the +x axis.
Given: x = -86, y = 75.
tanA = 75/-86 = -0.8721,
A = -41.09 deg.
-41.09 is in 4th quad., but our vectors are in 2nd quad. so we add 180
deg:
-41.09 + 180 = 138.9 deg.
To find the angle between the direction of the vector and the positive direction of x, we can use trigonometry.
First, let's find the tangent of the angle. The tangent of an angle can be found using the formula:
tan(angle) = y component / x component
In this case, the y component is +75.0 units and the x component is -86.0 units. So we have:
tan(angle) = 75.0 / -86.0
Next, we can use the inverse tangent function to find the angle:
angle = atan(tan(angle))
Using a calculator or a programming language, we can find the value of the angle.
Finally, we need to consider the convention that positive angles are measured counterclockwise from the +x axis and negative angles are measured clockwise from the +x axis. Since the x component is negative, the angle we found will also be negative.
Therefore, the answer is the negative angle we calculated using the tangent function.
To find the angle between the direction of the vector and the positive direction of x, you can use the trigonometric formula:
θ = tan^(-1)(y/x)
where θ is the angle, y is the y-component of the vector, and x is the x-component of the vector.
Given that the x component of the vector is -86.0 units and the y component is +75.0 units, we can substitute these values into the formula:
θ = tan^(-1)(75.0 / -86.0)
Now let's calculate it step by step:
Step 1: Calculate the ratio y/x:
y/x = 75.0 / -86.0 = -0.872093023
Step 2: Use the inverse tangent function (tan^(-1)) to find the angle:
θ = tan^(-1)(-0.872093023)
Using a calculator, you will find that:
θ ≈ -41.8 degrees
Therefore, the angle between the direction of the vector and the positive direction of x is approximately -41.8 degrees.