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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