# Reciprocal of cos?

Why 1 divided by cos(pi/4)=cos(-pi/4)?
Is it wrong to say 1/cos(pi/4)=sec(pi/4)?

Thanks

Buzz Bloom
Gold Member
Hi ryan:

Is it wrong to say 1/cos(pi/4)=sec(pi/4)?​
1/cos(pi/4)=sec(pi/4) is correct.

Why 1 divided by cos(pi/4)=cos(-pi/4)?​
I think you are asking: Why is the following correct?
1/cos(pi/4) = 1/cos(-pi/4)?​
If this is what you are asking, the reason that is correct is because
cos(pi/4) = cos(-pi/4),​
which is because
the cos function is symmetrical,​
and because
the reciprocal of two equal numbers will be equal.​

BTW: The title of the thread does not match your question. The inverse of the cos is the arccos, which is not the same as the reciprocal, 1/cos.

Regards,
Buzz

Last edited:
Thanks you

Mark44
Mentor
BTW: The title of the thread does not match your question. The inverse of the cos is the arccos, which is not the same as the reciprocal, 1/cos.
The thread title is now "Reciprocal of cos".

Hello,

1/cos(pi/4) is not equal to cos(-pi/4). Cos(-pi/4) is equal to cos(pi/4). It is because cos function is an even function and it produces same answer to negative and positive values. I can give you a simple reason that 0 and 2pi is same in angles and 0-pi/4 is same as 2pi-pi/4 if you see graph paper, rotate a line from positive X-axis in anti-clock wise direction it lies in fourth quadrant. Now, you see x co-ordinate is positive and hypotenuse is length so it's positive. Hence, base/hypotenuse is positive.