Examples using Inverse trigonometric functions

In this video I show you how to find the exact values of the following without using a calculator. You need to be familiar with the graphs of y=arcsin(x), y=arccos(x) and y=arctan(x) and also the quadrant diagram.


Find the value of:

  1.     \[{\rm{sin}}\left( {{\rm{arccos}}\frac{{\rm{3}}}{{\rm{4}}}} \right)\]

  2.     \[\cos \left( {\arctan \frac{3}{5}} \right)\]

  3.     \[\tan \left( {\arcsin -\frac{5}{6}} \right)\]


In this video I extend the work covered so far with finding the values of general expressions

Find the value of:

  1.     \[\cos \left( {\arcsin x} \right)\]

  2.     \[\sin \left( {\arctan x} \right)\]

  3.     \[\tan \left( {\arccos x} \right)\]


In this video I show you how to prove that following. Have a go before looking at the video.

    \[\arcsin x + \arccos x = \frac{\pi }{2}\]

This may not be the only method. If you have others then let me know and we can share them.

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