Expand Using Sum/Difference Formulas sin(15 degrees )

Problem

sin(15)

Solution

1. Identify two angles with known trigonometric values whose difference is 15

15=45−30

2. Apply the formula for the sine of a difference, which is sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

sin(45−30)=sin(45)*cos(30)−cos(45)*sin(30)

3. Substitute the exact values for the sine and cosine of 45 and 30

sin(45)=√(,2)/2

cos(30)=√(,3)/2

cos(45)=√(,2)/2

sin(30)=1/2

4. Multiply the terms together.

sin(15)=√(,2)/2⋅√(,3)/2−√(,2)/2⋅1/2

sin(15)=√(,6)/4−√(,2)/4

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

sin(15)=(√(,6)−√(,2))/4

Final Answer

sin(15)=(√(,6)−√(,2))/4

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