Find the Value Using the Unit Circle sin((7pi)/2)

Problem

sin((7*π)/2)

Solution

1. Identify the angle (7*π)/2 and determine its position on the unit circle by finding a coterminal angle within the standard range [0,2*π)

2. Subtract multiples of 2*π (which is (4*π)/2 from the given angle to simplify it.

(7*π)/2−2*π=(7*π)/2−(4*π)/2

(7*π)/2−(4*π)/2=(3*π)/2

3. Locate the angle (3*π)/2 on the unit circle, which corresponds to the point (0,−1)

4. Determine the sine value by identifying the ycoordinate of the point on the unit circle.

sin((3*π)/2)=−1

Final Answer

sin((7*π)/2)=−1

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