00:01
For this problem, we're asked to evaluate the six trig functions with the given angle, and the angle in the chart where we have blinks is negative 2 pi over 3.
00:10
And to evaluate a little easier using the unit circle, i'm going to find a co -terminal angle with negative 2 pi over 3, which would give us the same evaluations.
00:17
And i'll find that by adding a 2 pi full revolution, and 2 pi with a denominator of 3 would be 6 pi over 3.
00:25
So negative 2 pi over 3 plus 6 pi over 3 gives me 4 pi over 3.
00:30
So at the angle of 4 pi over 3, if i can find the x and y values, then i can find all these evaluations, because sine is the y value, cosine is the x value, tangent is the ratio of y over x, cotangent is the reciprocal of tangent, which means it's x over y, secan is the reciprocal of cotangue, or excuse me, cosine, which is 1 over x, and co -seekin is a reciprocal of sine, which means it's 1 over y.
00:54
So if we have the x and y point, then we have everything we need to evaluate.
00:58
And at our angle of 4 pi over 3 in the unit circle, that gives us an ordered pair of negative 1 half, negative square root 3 over 2.
01:09
And so now to do all our valuations, we're just going to appropriately match up what value we need or what ratio we need.
01:16
The sign of our angle would be equal to the y value, negative square root 3 over 2.
01:21
The cosine of our ankle would be equal to negative 1 1⁄2, the x value...