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.

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page. csc 4𝜋/3

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. We are looking for the value of the Koi can of seven pie divided by six. We have four answer choices. A is negative two B is negative one half C is one half D is two. So when we look at the coast sea camp of seven pi divided by six T, in this case would be seven pi divided by six. Referencing that on my unit circle, I find that the coordinates that match that are negative radical three divided by two and negative one half. From there. I recall that using a unit circle, my X value is the cosine of T. So the cosine of seven pi divided by six and my Y value is the sign of T or sign of seven pi divided by six. In this case, this is gonna help us because you can recall that co C can of any angle is equal to one divided by the sign of that angle. So the sea can of seven pi divided by six is going to be equal to one divided by the sign of seven pi divided by six which is negative one half. Simplifying my complex fraction. Here I have one divided by negative one half. Recalling the rules of fractions, I have to multiply by the reciprocal. So I have one multiplied by negative 2/1 which is the same as negative two, one multiplied by negative two is negative two. So the C camp of seven pi divided by six is answer choice. A negative two have a nice day.

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