Signs of the Trigonometric Functions Video Lecture | Mathematics (Maths) Class 11 - Commerce

hey how's it going for this video we're
gonna work on finding the signs of
different training metric functions
using a wonderful neat little tool that
I picked up when I was in school alright
so you may have seen this before maybe
not but this is actually a great way
that you can easily memorize whether
something like sine or cosine should be
positive or negative that's what I mean
by the signs of the trigonometric
functions so let's learn this real quick
and see exactly what information it
gives us so when you're doing different
trigonometric functions like sine of 23
degrees you get a number and the idea is
is this thing going to be positive or
negative and the clue to really figure
out well is it positive or negative is
depending on where that angle ends up is
that in quadrant one quadrant two
quadrant three or quadrant four if you
know what quadrant it's going to be in
then you can easily figure out what the
sine is going to be now these letters
here tell you which trigger
trigonometric functions are going to be
positive or negative for example if my
angle ends up in this first quadrant
then all the trigonometric functions are
going to be positive so if I'm dealing
with sine of 23 degrees sure enough
that's in the first quadrant oh I know
that's going to be a positive value when
I get over here to quadrant number two
then I know that sine and it's
reciprocal are going to be positive what
about the rest what about tangent and
cosine those will be negative so these
are telling me what values are what
trigonometric functions are going to be
positive so sine and it's reciprocal
what you know what we'll go ahead and
write out cosecant will also be the
other positive one all right moving on
whose going to be positive in the third
quadrant well T we don't have one
trigonometric function that starts with
T that's our tangent and if you want to
remember cotangent is the other one so
tangent and it's reciprocal and then the
last one who gets to be positive over
here cosine and it's reciprocal function
secant
so now that you know which functions
will be positive in which quadrant how
can you remember this really quickly
well a great mnemonic for this is to
remember that all students take calculus
and you mark them off in the order of
the quadrants so quadrant one is all
quadrant two is students quadrant three
is take and quadrant four is our
calculus so all students take calculus
and now you know which turn metric
functions are associated with them now
let's take this one step further and
actually try an example now that we have
this wonderful little thing down and
just out this out I'm gonna draw this in
the corner which is something you can do
if you're taking a quick test or
something you know quickly sketch this
out so all students take calculus we'll
use that to help us figure out what's
going on so the goal with this problem
here is to figure out what quadrant our
angle has ended up in and the only thing
we know is a little bit about the sine
of the functions so I know that if I
plug my angle into sine its negative and
if I plug my angle into tangent it it
turns out to be positive so where did
that angle go well if I know that sine
is negative then I immediately can rule
out the first and second quadrant
because in the first quadrant
everyone's positive and then the second
quadrant sine is positive and I
specifically know it's negative so it's
got to be on this lower half here I'm
gonna shade that in so so far our angle
has to be down here somewhere now the
next bit of information is that tangent
is positive so let's see where's tangent
positive wells positive in the first
quadrant that's positive in the third
quadrant so two bits so it could be here
or it could be down here
now there's only one quadrant where both
of these things are happening and sure
enough that is quadrant number three so
what quadrant is my angling I can say
theta
is in Quadrant three so this really
gives you information or a little hint
about that angle let's do it again so
this time cosine is negative and
cosecant is positive so Co cosine is
negative so that rules out those two i
need where it's negative so i know that
it has to be over on this side somewhere
over here so that cosine is negative
cosecant greater than zero now I have to
be careful
this is stands for all trigonometric
functions sine tangent and cosine or
worse where's cosecant is ko seeing it
up here you also have to remember that
these apply to their reciprocal
identities so cosecant is the reciprocal
of sine so cosecant of angle is equal to
one of the words sine of the angle so
I'm gonna use so it has to have the same
sign as sine of the angle so where is
sine positive sine is positive
up on the upper half here so let's shade
in the upper half all right now just
like before there's only one place where
both of these conditions happen
simultaneously and now I know where my
angle is theta is in Quadrant number two
so you know don't be afraid to write
this on your piece of paper if you need
a quick reference and it really gives
you a lot of intuition on the the sign
that these trigonometric functions
should have all right if you'd like to
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