Questions: Express the trig ratios as fractions in simplest terms.

$Express the trig ratios as fractions in simplest terms.$

Transcript text: Express the trig ratios as fractions in simplest terms.

Solution

Solution Steps

Step 1: Identify the given information

We are given a right triangle $\triangle CDE$ with the following side lengths: $CE = 15$ $CD = 8$ $DE = 17$ Angle $C$ is a right angle.

Step 2: Find sin(D)

$\sin(D) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{CE}{DE} = \frac{15}{17}$

Step 3: Find cos(D)

$\cos(D) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{CD}{DE} = \frac{8}{17}$

Step 4: Find tan(D)

$\tan(D) = \frac{\text{opposite}}{\text{adjacent}} = \frac{CE}{CD} = \frac{15}{8}$

Step 5: Find sin(E)

$\sin(E) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{CD}{DE} = \frac{8}{17}$

Step 6: Find cos(E)

$\cos(E) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{CE}{DE} = \frac{15}{17}$

Step 7: Find tan(E)

$\tan(E) = \frac{\text{opposite}}{\text{adjacent}} = \frac{CD}{CE} = \frac{8}{15}$

Final Answer

$\sin(D) = \frac{15}{17}$ $\cos(D) = \frac{8}{17}$ $\tan(D) = \frac{15}{8}$ $\sin(E) = \frac{8}{17}$ $\cos(E) = \frac{15}{17}$ $\tan(E) = \frac{8}{15}$

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