SOLUTION: find all values of t in [0, 2 pi] such that absolute value sec t = 1. I only found 0.

Algebra ->  Trigonometry-basics -> SOLUTION: find all values of t in [0, 2 pi] such that absolute value sec t = 1. I only found 0.       Log On


   

Question 1004703: find all values of t in [0, 2 pi] such that absolute value sec t = 1.
I only found 0.
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28sec%28t%29%29+=+1

abs%281%2F%28cos%28t%29%29%29+=+1

1%2F%28cos%28t%29%29+=+1 or 1%2F%28cos%28t%29%29+=+-1

------------------------------------------------

Let's focus on solving 1%2F%28cos%28t%29%29+=+1

1%2F%28cos%28t%29%29+=+1

1+=+1%2Acos%28t%29

1+=+cos%28t%29

cos%28t%29+=+1

t+=+0 or t+=+2pi

------------------------------------------------

Let's focus on solving 1%2F%28cos%28t%29%29+=+-1

1%2F%28cos%28t%29%29+=+-1

1+=+-1%2Acos%28t%29

1+=+-cos%28t%29

-cos%28t%29+=+1

cos%28t%29+=+-1

t+=+pi

------------------------------------------------

The three solutions to abs%28sec%28t%29%29+=+1 in the interval [0,2pi] are t+=+0, t+=+pi or t+=+2pi

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i found 3.

you can see them on the following graph that is displaying the absolute value of secant(x).

secant is equal to 1 / cosine.

if the cosine is 1, then the secant will be 1/1 = 1.

if the cosine is -1, then the secant will be 1/-1 = 1

if you graph cosine(x), you will see that cosine(x) is equal to 1 at x = 0 and 2pi, and cosine(x) is equal to -1 at x = pi.
the graph is shown below:

$$$

if you graph the absolute value of cosine(x), you will see that the absolute value of cosine(x) is equal to 1 at x = 0, pi, and 2pi.

$$$

if you graph secant(x), you will see that the secant is 1 at x = 0 and 2pi, and it is equal to -1 at x = pi.

$$$

if you graph absolute value of secant(x), you will see that the absolute value of secant(x) is equal to 1 at x = 0, pi, and 2pi.

$$$