00:01
Okay, so we are asked to find the six trigonometric ratios for the angle negative 7 pi over 6.
00:08
So first of all, where is negative 5 pi over 6 located? so if we are a negative angle, we are going counterclockwise around the circle.
00:17
If we land at negative pi, it's the same as negative 6 pi over 6.
00:21
So we're going 1 pi over 6 past 6 pi over 6.
00:25
So this angle is negative 7 pi over 6.
00:28
It is coterminal with the angle 5 pi over 6, and the reference angle here is pi over 6, and we're in quadrant 2.
00:38
So we're looking at this ordered pair, x and y, on the unit circle that negative 7 pi over 6 has as its ending point.
00:52
For the unit circle, the sign is the y value, cosine is the x value, tangent is y divided by x, and then your reciprocal functions flip those fractions.
01:03
So let's go ahead and find sine, cosine, and tangent for negative 7 pi over 6.
01:08
The sign of negative 7 pi over 6 is going to be the y value, which is 1 half.
01:16
Therefore, the co -secant of negative 7 pi over 6 is going to be the reciprocal of that, which is just 2...