i have to work out the forces i got the y- axis to be 8.37N and x-axis to be -0.73. when i do tan-1, i get -85.03. but the answer is 94.97. i think u have to add 180, but i dont know why? please help
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Correct, you have to add 180.
The problem is that there is no difference between the fractions y / −x or −y / x.
You can check for yourself: 8.37 / −0.73 = −116.5 and −8.37 / 0.73 = −116.5.
So when you do tan-1(−116.5), it is ambiguous which point and angle that you want your calculator to calculate: the one with the negative X or the one with the negative Y?
For this reason, the inverse tan on your calculator will always assume the one with positive X, in other words, the point laying in the 1st (+X, +Y) or 4th (+X, −Y) quadrant. This will always result in an angle between −90 and 90.
Since your point lays in the 2nd quadrant (−X, +Y), you have to add or subtract 180 to or from the result. The same applies when it is in the 3rd quadrant (−X, −Y).
The problem is that there is no difference between the fractions y / −x or −y / x.
You can check for yourself: 8.37 / −0.73 = −116.5 and −8.37 / 0.73 = −116.5.
So when you do tan-1(−116.5), it is ambiguous which point and angle that you want your calculator to calculate: the one with the negative X or the one with the negative Y?
For this reason, the inverse tan on your calculator will always assume the one with positive X, in other words, the point laying in the 1st (+X, +Y) or 4th (+X, −Y) quadrant. This will always result in an angle between −90 and 90.
Since your point lays in the 2nd quadrant (−X, +Y), you have to add or subtract 180 to or from the result. The same applies when it is in the 3rd quadrant (−X, −Y).