Find the Value Using the Unit Circle sin(30 degrees )

Problem

sin(30^∘)

Solution

1. Identify the angle on the unit circle. The angle 30^∘ corresponds to the point in the first quadrant where the terminal side intersects the unit circle.

2. Recall the coordinates for 30^∘ on the unit circle. The coordinates (x,y) for this angle are (√(,3)/2,1/2)

3. Apply the definition of the sine function. On the unit circle, sin(θ) is equal to the ycoordinate of the point.

4. Extract the yvalue from the coordinates. Since the ycoordinate is 1/2 the value of the sine function is 1/2

Final Answer

sin(30^∘)=1/2

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