While I'm solving for the angle between the vectors A = 10j+2k and B = -4j+0.5k,using dot product I got 161.5 degrees and using cross product I got 18.43 degrees.

The correct answer was 161.5 degrees.

sin(161.5) = 0.3173046

But arcsin(0.3173046) = 18.5

Could someone explain this??

  • 1
    $\begingroup$ I don't think I agree with closing this question. Although it asks about a specific computation, it does show an attempt, and the answer touches on an underlying concept that has educational value about vectors and trig used extensively in physics. It may have belonged better on Mathematics, but still fits here. $\endgroup$
    – RC_23
    Aug 7, 2022 at 19:09

1 Answer 1


The arcsine function on a calculator or computer will only return values between -90° and 90°. You have to add 180° to your answer of -18.5 to get the correct result of 161.5.

Arccosine returns values between 0 and 180°, which was why your dot product result was correct.

  • 3
    $\begingroup$ Indeed. Always a good idea to do a sketch of the vectors in this type of question. This makes it visually clear that the larger value of arcsine is the correct one. $\endgroup$
    – gandalf61
    Aug 7, 2022 at 16:58

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