Questions: Enter your answer as an improper fraction if necessary, and only enter the numerical value. For example, if the answer were sec B = 3/2, you would just enter 3/2 in the answer field.

Enter your answer as an improper fraction if necessary, and only enter the numerical value. For example, if the answer were sec B = 3/2, you would just enter 3/2 in the answer field.
Transcript text: 5.3 Six Trigonometric Ratios Enter your answer as an improper fraction if necessary, and only enter the numerical value. For example, if the answer were $\sec B=\frac{3}{2}$, you would just enter $\frac{3}{2}$ in the answer field.
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Solution

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Solution Steps

Step 1: Identify the given information

We are given a right triangle with sides BC = 12, AC = 35, and AB = 37. We are asked to find the six trigonometric ratios for angle B.

Step 2: Define the six trigonometric ratios

For angle B in a right triangle:

  • sine (sin B): opposite side / hypotenuse = AC / AB
  • cosine (cos B): adjacent side / hypotenuse = BC / AB
  • tangent (tan B): opposite side / adjacent side = AC / BC
  • cosecant (csc B): hypotenuse / opposite side = AB / AC
  • secant (sec B): hypotenuse / adjacent side = AB / BC
  • cotangent (cot B): adjacent side / opposite side = BC / AC
Step 3: Calculate the six trigonometric ratios

Using the given side lengths:

  • sin B = 35/37
  • cos B = 12/37
  • tan B = 35/12
  • csc B = 37/35
  • sec B = 37/12
  • cot B = 12/35

Final Answer:

sin B = 35/37, cos B = 12/37, tan B = 35/12, csc B = 37/35, sec B = 37/12, cot B = 12/35

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