Angels for vector calculations

[missakalla7977]

Hi there,
I am just wondering how do we go about figuring the values of different trginometric angles for the vector analysis problems?
For instance if we've to find the angle between the resultant and the x-axis, we use the tan formula but without a calculator, I am not sure how to about with it. For example, tan value of 3. That's almost impossible without a calculator unless there's another way...
How can we figure out those values without a calculator?

[mcat_premed3832]

There are 2 triangles (with the relationship of their sides) that you are expected to memorize: (1) the 30-60-90 triangle and (2) the 45-45-90 triangle (Chapter 1 in the GS) or see here: http://www.goldstandard-mcat.com/physics-equation-lists/

Besides that, you should know the function of angles like 0, 90 and 180 degrees. Of course you must be comfortable with estimating: you surely would not be concerned if you saw the cosine of 88 degrees on the MCAT since the answer would be clear by looking at the options.

In other words, even in your example of the tangent of 3, of course you can't calculate it with precision without a calculator; however, only based on what you are expected to know, you would be able to quickly narrow it down to the right answer based on the options provided to you.