Cos(-pi/4) & Sec(pi/4): What's the Difference?

[ryanuser]

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]

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.​

I hope this is helpful.

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

 

[ryanuser]

Thanks you

 

[Mark44]

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".

 

[Shehbaj singh]

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.

I hope this one helps and if any other query regarding my answer please ask.