What is sec^-1 (0) = to?

Question

Please help me!

Oh, and I also cant figure this one out:

csc^-1 (2 radical (3) / 3) = ????????

I do not like trig :(

Answer 1

The answers given so far(first 2) are wrong!
Let's tackle the first one:
You are looking for an angle whose secant is 0.
Let x = sec^-1 (0).
Then sec x = 0.
But the reciprocal of sec x is cos x, so
1/cos x = 0,
and
cos x is undefined. There is no such angle!!

The second one is done the same way:
Let x = csc^-1 (2√3/3)
csc x = 2√3/3.
The reciprocal of csc x is sin x, so
sin x = 3/(2√3) = √3/2.
So a value of x is 60 degrees.
(There are infinitely many others--the
only other one less than 360 degrees is 120 degrees)
Trig is a lot of fun if you learn your basics. Sorry
to hear you don't like it!

Answer 2

as you know domain of cos x is from -1 to +1
thus
-1 ≤ Cos x ≤ +1

sec x = 1 / cos x

so as you see very clearly

-∞ < sec x ≤ -1 and 1 ≤ sec x < ∞

and 0 is not a value for sec

we can clarify this more
if x = sec^-1 (0)
sec x = 0
1 / cos x = 0
so cos x should be infinite.
you clearly know that
-1 ≤ Cos x ≤ +1
so infinite is not a value for cos
so 0 is not a value for sec
thus sec^-1 (0) equals to nothing



cosec^-1 (2√3 / 3 )
= cosec^-1 (2 / √3 )

if the answer is x
x = cosec^-1 (2 / √3 )
cosec x = 2 / √3

1 / sin x = 2 / √3
Sin x = √3 / 2
x = 60°

Answer 3

The inverse of sec is cos because sec = 1/cos

sec^-1(0) = cos (0)
cos(0) = 1

In the same way the inverse of csc is sin

csc-1(2 radical (3)/3) = sin (2 radical (3)/3)

Answer 4

sec x = 1/cos x

Therefore sec^1 x = cos x

sec^1 (0) = cos (0) = 1

Hope this helps :-)