00:01
Let's begin with the pythagorean identity, sine squared t plus cosine squared t is equal to one.
00:11
Also note that sine t over cosine t is the same thing as tangent t.
00:21
All right, so we're going to write our sine square t.
00:26
We know we have a cosine value of negative two -fifths.
00:31
That quantity is squared minus one.
00:33
So we're going to rewrite the sine squared t plus, well, anytime we square a negative is going to be positive.
00:43
So two squared is four.
00:45
Five squared is 25.
00:46
We're going to set that equal to one.
00:49
We need to solve for sine squared t.
00:52
So we're going to subtract the 4 .25s from both sides.
00:56
Now we need common denominator.
00:59
That denominator is going to be 25.
01:01
So that means this one is rewritten as.
01:04
25 25ths.
01:06
We rewrite the 4 .25s and we keep the or rewrite the sign square t.
01:15
Now we evaluate.
01:18
So here we have 25 minus 4 to give us 21 and we have and we keep our denominator because we're subtracting.
01:26
So that stays at 25.
01:28
So here we have sine square t is equal to this quantity here, but we want just sine t.
01:34
So we're going to take the square root of b...