sin30cos30

sin30cos30 refers to the product of the sine of 30 degrees and the cosine of 30 degrees. In trigonometry, these values are well-defined. The sine of 30 degrees (sin 30°) is 1/2, and the cosine of 30 degrees (cos 30°) is the square root of 3 divided by 2 (√3/2).

Therefore, sin30cos30 is calculated by multiplying these two values: (1/2) * (√3/2). This multiplication results in √3/4. This value is an exact numerical representation of the product.

Alternatively, the trigonometric identity sin(2θ) = 2sinθcosθ can be used. If we let θ = 30°, then sin(2 * 30°) = sin(60°) = 2 * sin(30°) * cos(30°). We know that sin(60°) is equal to √3/2. Thus, √3/2 = 2 * sin30cos30. Dividing both sides by 2 gives sin30cos30 = (√3/2) / 2, which simplifies to √3/4. This confirms the result obtained through direct multiplication. The value √3/4 is approximately 0.433.