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Trigonometric relationship (Posted on 2008-09-19) Difficulty: 2 of 5
Find the relationship between arcsin[cos(arcsin x)] and arccos[sin(arccos x)].

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Solution from inside out -- spoiler Comment 2 of 2 |
cos(arcsin(x)) and sin(arccos(x)) are each sqrt(1-x^2), in the domain of x between -1 and 1, and thus always non-negative.

arcsin and arccos of the same value always produce complementary angles, so the two formulae under consideration produce complementary answers, adding to 90 if done in degrees, or pi/2 if done in radians. The domain remains -1 to 1, inclusive.

Edited on September 19, 2008, 1:07 pm
  Posted by Charlie on 2008-09-19 13:06:13

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