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.

cos 2𝜋/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. In this example, we want the value of the cosine of five pi divided by three, we are given four answer choices. So if we have the cosine of five pi divided by three, here T is gonna be five pi divided by three. So checking my unit circle that looks like it gives me the coordinates of one half, negative radical three halves. Recall that when we're using a unit circle, the X value of the coordinates is the cosine of T. So the cosine of five pi divided by three and the Y value is the sign of T. So in this case, the sign of five pi divided by three, since we are looking for the cosine of five pi divided by three, we have no further math. We need to do just looking at our X value just one half. So the cosine of five pi divided by three is one half which is answer choice. C have a nice day.

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