The x component of a vector A is -96.0 m and the y component is +29.0 m.
What is the angle between the direction of A and the positive direction of x?
tanA = y/x = 29.0/-96.0
Note that it is in QII
To find the angle between the direction of a vector A and the positive direction of x, you can use the inverse tangent function (or arctangent function). The formula for this is:
θ = arctan(y/x)
where θ is the angle, y is the y-component of the vector, and x is the x-component of the vector.
In this case, the y-component is +29.0 m and the x-component is -96.0 m.
θ = arctan(29.0 m / (-96.0 m))
To find this angle, you can use a scientific calculator or an online trigonometric calculator. If you enter the above expression into a calculator, it will give you the angle θ.
Note that the angle obtained will typically be in radians. If you want the result in degrees, you can convert it by multiplying by (180/π).
So, to summarize:
1. Calculate the ratio of the y-component to the x-component: y/x.
2. Use the arctan function to find the angle: arctan(y/x).
3. If needed, convert the angle from radians to degrees by multiplying by (180/π).