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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