Question

If \( \tan \theta = \frac{8}{15} \), then the value of \( \csc \theta \) will be:

• A. \( \frac{17}{8} \)
• B. \( \frac{8}{17} \)
• C. \( \frac{4}{3} \)
• D. \( \frac{15}{17} \)

Hint:

To find \( \csc \theta \), use the identity \( \csc \theta = \frac{\text{Hypotenuse}}{\text{Opposite}} \).

Answer 1

The Correct Option is A

Step 1: Use the identity for \( \csc \theta \).
We are given that \( \tan \theta = \frac{8}{15} \). Using the identity: \[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{8}{15} \]
Step 2: Find the hypotenuse using Pythagoras theorem.
The sides of the right triangle are 8 (opposite) and 15 (adjacent). To find the hypotenuse, \( h \), we use the Pythagoras theorem: \[ h = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \]
Step 3: Calculate \( \csc \theta \).
Now, we use the identity \( \csc \theta = \frac{h}{\text{Opposite}} \): \[ \csc \theta = \frac{17}{8} \]
Step 4: Conclusion.
Thus, the value of \( \csc \theta \) is \( \frac{17}{8} \). Therefore, the correct answer is (A).