2 Dimensional Force Addition (12/16)
The value "61 degrees" doesn't mean anything unless a reference frame is specified. On compasses used for navigation, North is the primary axis and all angles are given as degrees clockwise from North. In math class, the + x axis is the primary axis and all angles are given as degrees counter-clockwise from x. Both are valid, as are any other reference axes. Usually we'll just use an angle inside one of our force triangles and know that we tell if something is positive or negative from the direction its going in the picture.
That said, sines and cosines work if you use the angle from the positive x-axis. I've shown this with this picture. When you do the angle like this the calculator will give you whether you're talking about something in this reference frame to the left/down (negative) or to the right/up (positive).
To make your life easier, use these greater than 90 degree angles in this lab, because they're what you're reading directly off the protractor. The math that comes next will do so. We use the internal angle to decide which trig function to use (using SOH-CAH-TOA) and then directly plug the angle from the protractor in.
I was going to gloss over this detail in class, but two 8th period students during the 2016-17 school year wanted a mathematical justification of this, so we stayed after school and came up with this picture
2 Dimensional Force Addition (12/16)
The value "61 degrees" doesn't mean anything unless a reference frame is specified. On compasses used for navigation, North is the primary axis and all angles are given as degrees clockwise from North. In math class, the + x axis is the primary axis and all angles are given as degrees counter-clockwise from x. Both are valid, as are any other reference axes. Usually we'll just use an angle inside one of our force triangles and know that we tell if something is positive or negative from the direction its going in the picture.
That said, sines and cosines work if you use the angle from the positive x-axis. I've shown this with this picture. When you do the angle like this the calculator will give you whether you're talking about something in this reference frame to the left/down (negative) or to the right/up (positive).
To make your life easier, use these greater than 90 degree angles in this lab, because they're what you're reading directly off the protractor. The math that comes next will do so. We use the internal angle to decide which trig function to use (using SOH-CAH-TOA) and then directly plug the angle from the protractor in.
I was going to gloss over this detail in class, but two 8th period students during the 2016-17 school year wanted a mathematical justification of this, so we stayed after school and came up with this picture