In Exercises 5–18, the unit circle has been divided into twelve e...

Question

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋. 6 3 2 3 6 6 3 2 3 6 Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

tan 0

Accepted Answer

Hello, everyone. We are given a unit circle and asked to determine the value of the trigonometric function at the given real number T using the X Y coordinates in the diagram or specify that the expression is undefined. Here, we are looking for the value of the co tangent of zero. And our answer choices are a negative one B zero C one D undefined. So if we are looking for the cotangent of zero, that means our real number T here is zero. So looking at the unit circle for the value is zero, you won't see it explicitly but it does match with two pi because that is the start and end of our full rotation. So the coordinates at zero are 10. Recall that using a unit circle, our X value is the same as the cosine of T. So in this case, the cosine of zero and the Y value is the same as sine of T which in this case is sin of zero. So if we are looking for the cotangent of zero, we can say that this is the same as the cosine of zero divided by the sign of zero And when we do so the cosine of zero is one, the sign of zero is zero, any number divided by zero is undefined. So this means that the cotangent of zero is undefined, which is answer choice. D have a nice day.

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