Expand Using Sum/Difference Formulas cos(120)

Problem

cos(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 cosine of a sum, which is cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

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

cos(90^∘+30^∘)=cos(90^∘)*cos(30^∘)−sin(90^∘)*sin(30^∘)

4. Evaluate the trigonometric functions at these specific angles.

cos(90^∘)=0

cos(30^∘)=√(,3)/2

sin(90^∘)=1

sin(30^∘)=1/2

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

(0)*(√(,3)/2)−(1)*(1/2)

0−1/2

−1/2

Final Answer

cos(120^∘)=−1/2

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