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

Want more problems? Check here!