00:01
Okay, this question gives you one trig ratio and wants you to find the other five and you're given a quadrant.
00:09
So the first thing i'm going to do is say sine theta is three -fifths and i'm in between pi over two and pi.
00:16
So i'm back here.
00:17
Sign is three -fifths.
00:20
This is not on the unit circle because my radius is five.
00:24
So my y direction is three.
00:28
My hypotenuse is five.
00:29
So 345 makes a right triangle.
00:34
So my x direction is negative 4.
00:37
Cosine of theta is negative 4 .5ths.
00:41
Tangent of theta is y over x, negative 3 fourths.
00:49
Then i can do the reciprocal functions.
00:51
Cosecant is the reciprocal of sine.
00:55
Secant is the reciprocal of cosine.
01:00
And cotangent is the reciprocal of tangent.
01:06
Letter b, i'm given cosine, and i'm given that i am somewhere between negative pi and positive 3 pi over 2.
01:13
That's a lot of places.
01:16
So, cosine of theta is negative, both here and here.
01:23
I don't know the exact angle, but this is negative pi.
01:27
So the negative direction i can get to this triangle and the positive direction i can get to that triangle.
01:34
This one up here, i'll only get two in the positive direction.
01:39
But it doesn't matter how i get there as long as i get my triangle drawn.
01:42
So let me do a little cleaner job drawing it.
01:49
Negative 2 root 2 over 3.
01:54
A squared plus b squared equals c squared gives me a negative 1 here and a positive 1 here.
02:01
So sine theta could be either 1 3rd or negative 1 3rd, depending on which of the places i hit cosine, forward or backwards.
02:14
But that covers both cases.
02:16
Tangent of theta is plus or minus 1 over 2 root 2.
02:24
So cotangent of theta is plus or minus the reciprocal of tangent.
02:33
Cosecant of theta is the reciprocal of sign.
02:38
And secant of theta is the reciprocal of cosine.
02:46
So that takes care of parts a and b.
02:51
Now we need to look at part c.
03:00
Tangent theta is two -thirds...