00:01
This problem says evaluate the sine, cosine, and tangent of the angle without using a calculator.
00:05
And if the answer is undefined and are undefined, and we're asked to do this for negative 11 pi over 6 for sine cosine tangent.
00:12
And we're also asked to use a calculators to evaluate co -secant of 445 degrees.
00:17
So first for our negative 11 pi over 6, if we want to evaluate all these trig functions at this value, we could keep it in its negative form, but we can also find a coterminal angle to make it a little easier.
00:27
So what i'm going to do is add 2 pi to both sides, which is the same thing as adding 12 pi over 6 with a common denominator.
00:35
So negative 11 pi over 6 plus 12 pi over 6 gives us pi over 6, which means sine, cosine, and tangent of pi over 6 would give us the same evaluations as negative 11 pi over 6.
00:47
So sign of our angle pi over 6 is the y value at pi over 6 on the unit circle, and the y value at that angle is 1⁄2.
00:55
Cosine is the x value at our angle, and at pi over six, that would be square root 3 over 2.
01:01
Tangent is the ratio of y over x, or also the ratio of the sign of the angle over cosine of the angle...