How do I find Vector Resolution

F = 0.300 g N, theta = 60 degrees.

Do I take tan inverse (.3 sin 60/.3 cos 60)?

no need. They give you θ=60°

the vector is .3g*cos60°i + .3g*sin60°j

To find the vector resolution of a force, you can use trigonometry and the basic principles of vector addition. Here's how you can solve it step by step:

1. Start by drawing a diagram to represent the given information. You can draw a vector representing the force F, with its magnitude (|F|) equal to 0.300 g N and its angle (θ) equal to 60 degrees.

2. Determine the x-component and y-component of the force. The x-component (F_x) represents the horizontal component, and the y-component (F_y) represents the vertical component. You can use trigonometry to find these components:

F_x = |F| * cos(θ)
F_y = |F| * sin(θ)

In this case, F_x = 0.300 g N * cos(60 degrees) and F_y = 0.300 g N * sin(60 degrees).

3. Calculate the x-component and y-component separately. In your case, you can substitute the values:

F_x = 0.300 g N * cos(60 degrees)
= 0.300 * 0.5
= 0.150 g N

F_y = 0.300 g N * sin(60 degrees)
= 0.300 * 0.866
= 0.2598 g N

4. The vector resolution is then given by the x-component and y-component (F_x, F_y). In your case, the vector resolution is (0.150 g N, 0.2598 g N).

So, to answer your question, no, you do not take the tangent inverse of (0.3 * sin(60) / 0.3 * cos(60)). Instead, you use trigonometric functions to calculate the x- and y-components of the vector separately.