Find the Value Using the Unit Circle sin(285)

Problem

sin(285)

Solution

1. Identify the angle in the standard unit circle. The angle 285 is in the fourth quadrant because 270<285<360

2. Rewrite the angle using a sum or difference of common reference angles. We can express 285 as 240+45 or 330−45 Let's use 240+45

3. Apply the sine addition formula, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

4. Substitute the known values from the unit circle for A=240 and B=45

sin(240)=−√(,3)/2

cos(240)=−1/2

sin(45)=√(,2)/2

cos(45)=√(,2)/2

5. Calculate the result by plugging these values into the formula:

sin(285)=(−√(,3)/2)*(√(,2)/2)+(−1/2)*(√(,2)/2)

sin(285)=−√(,6)/4−√(,2)/4

6. Simplify the expression into a single fraction.

Final Answer

sin(285)=(−√(,6)−√(,2))/4

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