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Trigonometry: Trigonometric Functions

Problems

The Unit Circle

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Problem : If an arc of the unit circle has length , what is the measure of the central angle that intercepts that arc?

radians

Problem : The coordinates of a point on the unit circle are (0, sin(s) ). What is the value of s ?

sin(s) = 1 , so s = +2Πn , where n is an integer.

Problem : An angle in standard position intercepts the unit circle at (x, y) . The arc between (1,0) and (x, y) has length s . Solve for x and y in terms of s .

x = cos(s) , and y = sin(s)

Problem : The $x$-coordinate of a point on the unit circle is . What are the possible y-coordinates?

and .

Problem : Is the equation for the unit circle a function?

No. For a given input ( x -coordinate), there is more than one output ( y - coordinate). For example, when x = 0 , y = 1 and -1.

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