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What is the product of sinAcosB?

Published in Trigonometry 1 min read

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.

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