Solve sin 12° · sin 48° · sin 54°
Answer (1)
To solve the expression sin 1 2 ∘ ⋅ sin 4 8 ∘ ⋅ sin 5 4 ∘ , we may use trigonometric identities and properties to find its value.
One possible approach is to use known sine values and properties of complementary angles. However, calculating directly involves using a trigonometric identity known as the product-to-sum identity, which can simplify the product of two sine functions. Unfortunately, applying this identity to three angles directly isn't straightforward without known identities or calculators. Thus, this calculation may typically be tackled by numerical methods or using a calculator to get an approximate numerical value directly.
For example, using a scientific calculator:
sin 1 2 ∘ ≈ 0.2079
sin 4 8 ∘ ≈ 0.7431
sin 5 4 ∘ ≈ 0.8090
Multiplying these values:
( 0.2079 \cdot 0.7431 \cdot 0.8090 \approx 0.125 )
This provides an approximate numeric result. If a precise value is needed or if simplifications are desired, a more complex trigonometric manipulation or a mathematical software tool may be required.
