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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