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1 answer:

Radda [10]3 years ago

8 0

Answer: Option 4

CE/DE

Explanation:

Sin = Opposite/Hypotenuse

In triangle DCE the opposite ( angle D ) is CE and the hypotenuse is DE

so sinD = CE/DE

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aivan3 [116]

We will apply the "FOIL" method for multiplying two binomials. In this method you will:

The mathematical representation of the FOIL method is shown as:

$(a + b)(c + d) = ac + ad + bc + bd$

Let's apply the FOIL method.

The first two terms of each binomial are $\frac{4}{7}$ and $\frac{8}{7}$ . Multiplied together, we find the new term of $\frac{4}{7} \cdot \frac{8}{7} = \frac{4 \cdot 8}{7 \cdot 7} = \frac{32}{49}$ .
The outside two terms are $\frac{4}{7}$ and $\frac{7}{5} i$ . Multiplied together, these two terms are $\frac{4}{7} \cdot \frac{7}{5}i = \frac{4 \cdot 7}{7 \cdot 5}i = \frac{28}{35}i$ .
The inside two terms are $-i$ and $\frac{8}{7}$ . Multiplied together, these two terms are $- \frac{8}{7} i$ .
The last two terms are $-i$ and $\frac{7}{5} i$ . Multiplied together, these two terms are $-i \cdot \frac{7}{5}i = -\frac{7}{5} i^2$ . Remember though that $i^2 = 1$ , so our new term is actually $\frac{7}{5}$ .
Added together, we get: $\frac{32}{49} + \frac{28}{35} i - \frac{8}{7} i + \frac{7}{5} = \frac{160}{245} + \frac{196}{245}i - \frac{280}{245}i + \frac{343}{245} = \frac{503}{245} - \frac{84}{245} i = \frac{503}{245} - \frac{12}{35}i$ .