Write the sum as a product: $\sin(24.4p) + \sin(8.4p)$

Neetesh Kumar | October 16, 2024

Pre-Calculus Homework Help

Sum-to-Product and Product-to-Sum Formulas Assignment 9.4 Question 13
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Step-by-step solution:

We will use the sum-to-product identity for sines:

$\sin(A) + \sin(B) = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right)$

For $A = 24.4p$ and $B = 8.4p$:

1. Calculate $\frac{A + B}{2}$:

   $\frac{24.4p + 8.4p}{2} = 16.4p$

2. Calculate $\frac{A - B}{2}$:

   $\frac{24.4p - 8.4p}{2} = 8p$

Now apply the identity:

$\sin(24.4p) + \sin(8.4p) = 2 \sin(16.4p) \cos(8p)$

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Final answer:

$\boxed{2 \sin(16.4p) \cos(8p)}$

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