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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