Expand Using Sum/Difference Formulas sin(120)

Problem

sin(120)

Solution

1. Identify two angles that sum or subtract to 120 using standard values from the unit circle, such as 90 and 30

2. Apply the formula for the sine of a sum: sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

3. Substitute A=90 and B=30 into the formula.

sin(90+30)=sin(90)*cos(30)+cos(90)*sin(30)

4. Evaluate the trigonometric functions for the chosen angles.

sin(90)=1

cos(30)=√(,3)/2

cos(90)=0

sin(30)=1/2

5. Simplify the expression by performing the multiplication and addition.

(1)*(√(,3)/2)+(0)*(1/2)=√(,3)/2

Final Answer

sin(120)=√(,3)/2

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