Consider the vector v=-5.7i-7.2j
Approximate to the nearest tenth of degree the angle vector v makes with the positive horizontal direction?
theta=arcTan(7.2/5.7) and since it is in the third quadrant,
theta=arctan(7.2/5.7) + 180 degrees
Thanks for the help! I wanted to ask how did you know that we're supposed to divide (7.2/5.7) and not the other way around?
if the angle A is drawn in the standard position, tan(A) = y/x
To find the angle that the vector v makes with the positive horizontal direction, you can use trigonometry.
First, recall that the horizontal direction corresponds to the x-axis. Therefore, we need to find the angle that the vector v makes with the x-axis.
The formula to find the angle between a vector and the positive x-axis is given by:
θ = arctan(y/x)
Where θ is the angle, y represents the vertical component of the vector, and x represents the horizontal component of the vector.
In this case, the vertical component (y) of the vector v is -7.2, and the horizontal component (x) is -5.7.
Substituting these values into the formula:
θ = arctan(-7.2/-5.7)
Now, calculate the angle using a calculator or math software:
θ ≈ 52.6 degrees
Therefore, the vector v makes an angle of approximately 52.6 degrees with the positive horizontal direction.