Find the Exact Value sin(195)

Problem

sin(195)

Solution

1. Identify the angle as a sum or difference of special angles from the unit circle.

sin(195)=sin(150+45)

2. Apply the sum formula for sine, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

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

3. Substitute the known exact values for each trigonometric function.

sin(150)=1/2

cos(45)=√(,2)/2

cos(150)=−√(,3)/2

sin(45)=√(,2)/2

4. Multiply the terms together.

sin(195)=(1/2)*(√(,2)/2)+(−√(,3)/2)*(√(,2)/2)

sin(195)=√(,2)/4−√(,6)/4

5. Simplify the expression by combining the fractions over a common denominator.

sin(195)=(√(,2)−√(,6))/4

Final Answer

sin(195)=(√(,2)−√(,6))/4

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