00:02
Okay, we're given that the cosine of an angle is the square root of 21 over 7, and we're being asked to find the cosecant of that angle, which i just wrote a note that cosecant is the hypotenuse over opposite when you have a right triangle because it's the inverse of sine.
00:26
I mean, it's the reciprocal of sine.
00:28
So let me draw a just generic right triangle to represent our angle.
00:40
So let's say our angle is theta here.
00:47
So if the cosine is square root of 21 over 7, remember cosine was adjacent over hypotenuse, then i can call this adjacent sine square root of 21 and this hypotenuse is 7, and that could represent our trig ratio.
01:16
So now for cosecant, we know the hypotenuse, but we don't know the opposite side.
01:28
Let's call that x over here.
01:31
So we can solve for x using the pythagorean theorem because we know that square root of 21 squared plus x squared is going to equal 7 squared.
01:49
Hmm, see i'm out of room over here.
01:55
Let me rewrite that.
01:57
So square root of 21 squared plus x squared equals 7 squared.
02:05
And let me delete this here...