Expand Using Sum/Difference Formulas sin(225)

Problem

sin(225)

Solution

1. Identify two common angles from the unit circle that sum or differ to 225 We can use 180 and 45 since 180+45=225

2. Apply the sum formula for sine, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

3. Substitute the values A=180 and B=45 into the formula.

sin(180+45)=sin(180)*cos(45)+cos(180)*sin(45)

4. Evaluate the trigonometric functions for the specific angles.

sin(180)=0

cos(180)=−1

sin(45)=√(,2)/2

cos(45)=√(,2)/2

5. Simplify the expression by multiplying and adding the values.

(0)*(√(,2)/2)+(−1)*(√(,2)/2)

0−√(,2)/2

−√(,2)/2

Final Answer

sin(225)=−√(,2)/2

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