Question

Express the trig ratios as fractions in simplest terms.
C
D
E
36
60
48
Answer
Attempt 1 out of 2

cos EE =

sin DD =

cos EE and sin DD
are equal
because start overline, C, E, end overline
CE
is
opposite
∠EE and
adjacent to
∠DD .
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Answer 1

To help you express the trigonometric ratios as fractions in their simplest terms, we need to consider the triangle formed by the points provided (C, D, E) and the lengths of the sides.

Given the values:
- \(CE = 36\) (the side opposite to angle \(E\) or \( \sin E\))
- \(DE = 60\) (the side adjacent to angle \(D\) or \( \cos D\))
- \(CD = 48\) (the hypotenuse)

Let's calculate the trigonometric ratios:

1. **Cosine of angle E** (cos E):
\[
\cos E = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{CD}{CE} = \frac{48}{60}
\]
Simplifying:
\[
\cos E = \frac{48}{60} = \frac{4}{5}
\]

2. **Sine of angle D** (sin D):
\[
\sin D = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{CE}{CD} = \frac{36}{48}
\]
Simplifying:
\[
\sin D = \frac{36}{48} = \frac{3}{4}
\]

Since we have found the values, we can state:

\[
\cos E = \frac{4}{5}
\]
\[
\sin D = \frac{3}{4}
\]

Next, we can verify if \(\cos E\) and \(\sin D\) are equal. For them to be equal, the sine and cosine values need to match. However:
- \(\cos E = \frac{4}{5}\)
- \(\sin D = \frac{3}{4}\)

These values are not equal.

To conclude,
- \(\cos E\) = \( \frac{4}{5} \)
- \(\sin D\) = \( \frac{3}{4} \)

You can now submit the following answers:
- **cos EE = \(\frac{4}{5}\)**
- **sin DD = \(\frac{3}{4}\)**

And they are **not equal**.