111k views
5 votes
Which expression is equivalent to sin(1.8x) sin(0.5x)?

User Jebik
by
8.9k points

2 Answers

0 votes

Final answer:

The expression sin(1.8x) sin(0.5x) is equivalent to ½[cos(1.3x) − cos(2.3x)] using the product-to-sum trigonometric identity.

Step-by-step explanation:

The expression sin(1.8x) sin(0.5x) can be rewritten using a trigonometric identity known as the product-to-sum identity. Specifically, we will use the identity for the product of sines, which states that sin A sin B is equivalent to ½[cos(A − B) − cos(A + B)]. Applying this to our expression, we get:

sin(1.8x) sin(0.5x) = ½[cos(1.8x − 0.5x) − cos(1.8x + 0.5x)]

By simplifying the terms inside the cosine functions:

sin(1.8x) sin(0.5x) = ½[cos(1.3x) − cos(2.3x)]

This simplification results in an expression that combines two cosine waves with different frequencies. The product-to-sum formula is particularly useful in physics and engineering contexts, such as analyzing wave interference or signal processing.

User Haykart
by
8.3k points
2 votes
Hum, this problem was difficult. You use the next expression to solve this problem. \[\cos (A - B) = \cos A \cos B + \sin A \sin B \] \[\cos (A + B) = \cos A \cos B - \sin A \sin B\] \[\cos (A - B ) - \cos (A +B ) =2 \sin A \sin B\] So \[\sin A \sin B = 0.5 \left( \cos(A - B) - \cos(A + B) \right)\] A = 1.8 x, B = 0.5 x \[\sin (1.8x) \sin (0.5x) = 0.5\left( \cos(1.8-0.5)x - \cos(1.8+0.5)x \right)\]\[= 0.5 \left( \cos(1.3x) - \cos (2.3x) \right)\] It's finish !!
User ManueGE
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories