Expand Using Sum/Difference Formulas sin(30)

Problem

sin(30)

Solution

1. Identify the goal to represent 30 as a sum or difference of two common angles from the unit circle, such as 90−60 or 45−15 Using 90−60 is a standard choice.

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

3. Substitute A=90 and B=60 into the identity.

sin(90−60)=sin(90)*cos(60)−cos(90)*sin(60)

4. Evaluate the trigonometric values for the specific angles: sin(90)=1 cos(60)=1/2 cos(90)=0 and sin(60)=√(,3)/2

sin(30)=(1)*(1/2)−(0)*(√(,3)/2)

5. Simplify the expression to find the final numerical value.

sin(30)=1/2−0

sin(30)=1/2

Final Answer

sin(30)=1/2

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