3-2-45 secant inverse
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When doing this kind of problem, remember that whenever we see an
inverse, it means that it's an angle when it's a trig function.
So the secant inverse of -7 really, really says that's just
some angle.
So if we take the secant of each side, actually let's also
remember secants restricted to where secants restricted from
zero to π, because it has to be 1 to one.
Remember secant is the inverse of cosine.
So if we look at our cosine graph, we've got to cover all
the Y values always using zero to π halves in all six of them.
But I need all the Y values and if possible I want it to be on a
smooth continuous curve.
So I'm going to have from zero to π.
When we put in the actual secant graph, we would have this with
an asymptote everywhere.
We have an intercept for cosine.
And then here actually let's rewrite that as zero to π
halves.
And we can't include Pi halves because that's an asymptote and
then Pi halves to π.
So secant inverse of -7 really really is just an angle.
So then if I take the secant of each side, the secant and secant
inverse are going to give us -7 equals secant Theta.
But secant Theta we know is one over cosine.
So then I could think of that -7 / 1 cross multiply -7 cosine
Theta equal 1, cosine Theta would equal negative 1/7.
So on our calculator we would put in cosine inverse of -1
seventh.
So if we pull up our calculator and we tell it we want to go
into a calculator and I'm going to do cosine inverse of -1 / 7
control enter.
So if I go back to my menu key and look at my settings and
document setting, I can see I'm in degree mode.
If I needed to be in Radian mode, I would just change the
Radian.
I make it the default so it's true everywhere.
Go back to #4 arrow up, hit enter, control enter again.
So there it is in radians.
A different way is to actually use seek an inverse on the TI
inspire.
So if I do a control sign, I can actually put in -7 and then I
can arrow back and change this NIN to EC and do a control enter
again.
Another way still is to go to the book and the book and then
#2 has a trig listing.
And if we go to number 2 and then the trig, and then we want
inverse cosecant of -7.
So lots of different ways to oops, I needed secant, sorry.
OK, so go back to the book which is here inverse secant enter -7
control enter.
So lots of different ways to do it.
But to understand what's really happening, know that that's
really, really just an angle.
Take the secant of each side one over and then you can put it
into the calculator that way.