Expand Using Sum/Difference Formulas cos(195)

Problem

cos(195)

Solution

1. Identify two common angles from the unit circle that sum or subtract to 195 We can use 150 and 45 because 150 + 45 = 195$.

2. Apply the formula for the cosine of a sum, which is cos(α+β)=cos(α)*cos(β)−sin(α)*sin(β)

3. Substitute the values α=150 and β=45 into the formula.

cos(150+45)=cos(150)*cos(45)−sin(150)*sin(45)

4. Evaluate the trigonometric functions for the specific angles.

cos(150)=−√(,3)/2

cos(45)=√(,2)/2

sin(150)=1/2

sin(45)=√(,2)/2

5. Multiply the terms together.

(−√(,3)/2)*(√(,2)/2)−(1/2)*(√(,2)/2)

−√(,6)/4−√(,2)/4

6. Combine the fractions over a common denominator.

(−√(,6)−√(,2))/4

Final Answer

cos(195)=(−√(,6)−√(,2))/4

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