Question

Evaluate: sec(5pi/4)

Answer 1

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) = -$\frac{ \sqrt{2}}{2} ;$
Finally, sec (5pi/4) = -$\sqrt{2}.$

Answer 2

The evaluation should be $sec (5\pi\div 4) = -\sqrt{2}$

• The calculation is as follows:

We know that

The formula: $sec\ x = 1 \div cos\ x;$

Now,$sec\ (5\pi\div 4) = 1\div cos (5\pi\div 4);$

But, $cos (5\pi\div 4) = cos (\pi + \pi\div 4);$

Now We use the formula$cos (\pi + y) = - cos\ y;$

So, $cos (\pi + \pi\div 4) = -cos(\pi\div 4) =\sqrt{2} \div -2$

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