The product of sinAcosB is a trigonometric expression that cannot be simplified further without additional information.
Understanding the Expression
- sinA represents the sine of angle A.
- cosB represents the cosine of angle B.
The product of these two trigonometric functions is simply a multiplication: *sinA cosB**.
Applications
This expression appears in various trigonometric identities and formulas, including:
- Double Angle Formula: cos(2A) = 1 - 2sin²A = 2cos²A - 1
- Product-to-Sum Formula: sinAcosB = (1/2)[sin(A+B) + sin(A-B)]
Example
Let's say A = 30° and B = 45°. Then:
- sinA = sin(30°) = 1/2
- cosB = cos(45°) = √2 / 2
Therefore, the product sinAcosB would be:
(1/2) * (√2 / 2) = √2 / 4
Conclusion
The product of sinAcosB is a fundamental trigonometric expression that can be used in various calculations and formulas. Its value depends on the specific angles A and B.
