Calculating the exact value of an inverse

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Discussion Overview

The discussion revolves around calculating the value of the expression cos[ sin^-1 (1/2) + sin^-1 (-1) ]. Participants explore the use of inverse trigonometric functions and their properties, focusing on the mathematical reasoning behind the calculation.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks for help in calculating the expression involving inverse sine and cosine.
  • Another participant prompts for clarification on the formula for cos(a+b).
  • A participant expresses self-deprecation after realizing a mistake in their understanding.
  • One participant provides calculations showing that arcsin(1/2) equals π/6 and arcsin(-1) equals -π/2, leading to a sum of -π/3, and concludes that cos(-π/3) equals 1/2.

Areas of Agreement / Disagreement

The discussion includes a mix of questions, confirmations, and calculations, but does not indicate any explicit consensus on the overall approach or results.

Contextual Notes

Some assumptions about the properties of inverse trigonometric functions and their ranges may not be fully articulated, and there may be unresolved steps in the calculations presented.

trap
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cos[ sin^-1 (1/2) + sin^-1 (-1) ]

appreciate any help on this
 
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cos(a+b) = ?
 
ohh, yes, thanks, how dumb i am...
 
[tex]\arcsin \ \frac{1}{2}=\frac{\pi}{6}[/tex]

[tex]\arcsin \ -1=-\frac{\pi}{2}[/tex]

Add the 2 results and end up with [tex]-\frac{\pi}{3}[/tex]

And then
[tex]\cos \ -\frac{\pi}{3} =\frac{1}{2}[/tex]

Daniel.
 
Last edited:

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