Trigonometry of General Triangles and Trigonometric Functions — Test

Question 25 • Mathematics III

Which of the following best explains the value of sine pi over 3 on the given unit circle?

Answer

sine pi over 3 is equal to adjacent over hypotenuse is equal to adjacent over 1 is equal to adjacent The length adjacent to the angle is the horizontal distance from the y -axis on the graph.

sine pi over 3 is equal to opposite over hypotenuse is equal to opposite over 1 is equal to opposite The length opposite the angle is the vertical distance from the x -axis on the graph.

sine pi over 3 is equal to adjacent over hypotenuse is equal to adjacent over 1 is equal to adjacent The length adjacent to the angle is the vertical distance from the x -axis on the graph.

sine pi over 3 is equal to opposite over hypotenuse is equal to opposite over 1 is equal to opposite The length opposite the angle is the horizontal distance from the y -axis on the graph.

Explanation

On the unit circle, the hypotenuse has length 1, and sine is opposite divided by hypotenuse. For an angle of π/3, the opposite side is the vertical distance from the x-axis, so sine π/3 is that vertical distance (equal to √3/2). Choice A states this; the other choices either use the adjacent side or describe the wrong distance.

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