Respuesta :

crisforp
We have the formula: sec x = 1 / cos x;
Then, sec (5pi/4) = 1/ cos (5pi/4);
But, cos (5pi/4) = cos (pi + pi/4);
We use the formula: cos (pi + y) = - cosy;
Then, cos (pi + pi/4) = -cos(pi/4) = -[tex] \frac{ \sqrt{2}}{2} ;[/tex]
Finally, sec (5pi/4) = -[tex] \sqrt{2}.[/tex]

The evaluation should be [tex]sec (5\pi\div 4) = -\sqrt{2} [/tex]

  • The calculation is as follows:

We know that

The formula: [tex]sec\ x = 1 \div cos\ x;[/tex]

Now,[tex] sec\ (5\pi\div 4) = 1\div cos (5\pi\div 4);[/tex]

But, [tex]cos (5\pi\div 4) = cos (\pi + \pi\div 4);[/tex]

Now We use the formula[tex]cos (\pi + y) = - cos\ y;[/tex]

So, [tex] cos (\pi + \pi\div 4) = -cos(\pi\div 4) =\sqrt{2} \div -2 [/tex]

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