In a right triangle, what is the reciprocal of $\tan b$?

• A. $\sin b$
• B. $\cot b$
• C. $\csc b$
• D. $\sec b$

Answer: (B)

Verified step by step guidance

1. Recall the definition of the tangent function in a right triangle: \(\tan b = \frac{\text{opposite side}}{\text{adjacent side}}\).
2. The reciprocal of \(\tan b\) is the value you get when you flip the fraction, so it becomes \(\frac{\text{adjacent side}}{\text{opposite side}}\).
3. Recognize that the reciprocal of \(\tan b\) is the cotangent function, which is defined as \(\cot b = \frac{\text{adjacent side}}{\text{opposite side}}\).
4. Understand that \(\sin b = \frac{\text{opposite side}}{\text{hypotenuse}}\), \(\csc b = \frac{1}{\sin b}\), and \(\sec b = \frac{1}{\cos b}\), so these are not the reciprocals of \(\tan b\).
5. Therefore, the reciprocal of \(\tan b\) is \(\cot b\), which matches the correct answer.