Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the values of other five trigonometric functions of the following:

cosx space equals space minus 1 half comma space straight x lies in third quadrant

Answer

Here space space cosx space equals space minus 1 half
sinx<0, cosx<0, secx<0, cosecx<0, tanx>0, cotx>0         (∵  x lies in quadrant III)

Now,     sin squared straight x plus cos squared straight x space equals space 1   space space space rightwards double arrow space space space sin squared straight x plus 1 fourth equals 1 space space space space space space space space space space space rightwards double arrow space space space space space space space space space space sin squared straight x space equals space 3 over 4 space space space rightwards double arrow space space space sinx space equals space plus-or-minus fraction numerator square root of 3 over denominator 2 end fraction

rightwards double arrow                 sinx space equals space minus fraction numerator square root of 3 over denominator 2 end fraction                                       (∵ sinx is -ve)
                     secx space equals space 1 over cosx space equals space minus 2,                          cosecx space equals space 1 over sinx space equals space minus fraction numerator 2 over denominator square root of 3 end fraction comma
                      tanx space equals space sinx over cosx space equals space fraction numerator left parenthesis negative square root of 3 divided by 2 right parenthesis over denominator left parenthesis negative 1 divided by 2 right parenthesis end fraction space equals space square root of 3 comma     <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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