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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