Find the Exact Value sin(1050)

Problem

sin(1050)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is within the range [0,360)

1050−2⋅360=1050−720

1050−720=330

2. Identify the quadrant for 330 Since 270<330<360 the angle lies in Quadrant IV.

3. Determine the sign of the sine function in Quadrant IV. In this quadrant, sin(θ) is negative.

4. Calculate the reference angle θ′ for an angle in Quadrant IV using the formula θ′=360−θ

θ′=360−330=30

5. Evaluate the function using the reference angle and the determined sign.

sin(330)=−sin(30)

sin(30)=1/2

−sin(30)=−1/2

Final Answer

sin(1050)=−1/2

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