Find the Exact Value sin(45)cos(30)

Problem

sin(45)*cos(30)

Solution

1. Identify the exact value of sin(45) using the unit circle or a special right triangle (45−45−90.

sin(45)=√(,2)/2

2. Identify the exact value of cos(30) using the unit circle or a special right triangle (30−60−90.

cos(30)=√(,3)/2

3. Substitute these values into the original expression.

sin(45)*cos(30)=√(,2)/2⋅√(,3)/2

4. Multiply the numerators and the denominators to simplify the expression.

(√(,2)⋅√(,3))/(2⋅2)=√(,6)/4

Final Answer

sin(45)*cos(30)=√(,6)/4

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