Theta in converting sec to cos

  • Thread starter vanmaiden
  • Start date
  • #1
102
1

Homework Statement


I saw in my calculus book that something along the lines of arcsec [itex]\frac{4}{\sqrt{pi}}[/itex] = x was converted to arccos [itex]\frac{\sqrt{pi}}{4}[/itex] = x. I understand that sec and cos are reciprocals, but I don't see why has to be flipped as well.

Homework Equations


cos (θ), sec (θ)


The Attempt at a Solution


I began to think of the graphs and such, but I just can't think of why this works. I don't normally mess with the inverse trig functions and was hoping someone could point out what I'm missing.

Thank you.
 

Answers and Replies

  • #2
34,667
6,379

Homework Statement


I saw in my calculus book that something along the lines of arcsec [itex]\frac{4}{\sqrt{pi}}[/itex] = x was converted to arccos [itex]\frac{\sqrt{pi}}{4}[/itex] = x. I understand that sec and cos are reciprocals, but I don't see why has to be flipped as well.

Homework Equations


cos (θ), sec (θ)


The Attempt at a Solution


I began to think of the graphs and such, but I just can't think of why this works. I don't normally mess with the inverse trig functions and was hoping someone could point out what I'm missing.

Thank you.
Let x = [itex]sec^{-1}\frac{4}{\sqrt{\pi}}[/itex]
Then sec(x) = [itex]\frac{4}{\sqrt{\pi}}[/itex]
So cos(x) = [itex]\frac{\sqrt{\pi}}{4}[/itex]
Which means that x = cos-1[itex]\frac{\sqrt{\pi}}{4}[/itex]

It should be understood that there are domain restrictions on x.
 

Related Threads on Theta in converting sec to cos

Replies
2
Views
756
Replies
3
Views
1K
  • Last Post
Replies
7
Views
1K
Replies
4
Views
5K
Replies
6
Views
3K
Replies
7
Views
4K
Replies
1
Views
16K
Replies
2
Views
8K
Replies
3
Views
7K
Replies
1
Views
4K
Top