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. cos 3𝜋/2

Unit circle with coordinates for angles in radians, illustrating trigonometric functions.

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page. cos 3𝜋/2

Accepted Answer

Hello, everyone given a unit circle, we are asked to determine the value of the trigonometric function at the given real number T using the X Y coordinates in the diagram or specified that the equation is undefined. We want to find the value of the cosine of zero. And our answer choices are a negative one B zero C one D undefined. First thinking about the cosine of zero, I recall that using a unit circle, I am looking at these angles in standard position which means the value of zero shares a line with the value two pi because they would both start in the same spot. So the value that is given at two pi which is the same as zero is the 0.10. Next recall that when we are given coordinates from a unit circle, the X value stands for the cosine of the given angle T and the Y value stands for the sign of the given angle T. So since in this example, we are looking for the cosine of zero, this would be the cosine of T which is one. So the cosine of zero equals one because zero is RT in this case, so this is answer choice. C one have a nice day.

Key Concepts

Unit Circle

Trigonometric Functions

Radians

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