Multiple Choice
In right triangle xyz, if angle is a right angle and the side opposite angle has length , the side adjacent to angle has length , and the hypotenuse has length , what is ?
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2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In a right triangle, what is the reciprocal of ?
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Verified step by step guidance1
Recall the definition of the tangent function in a right triangle: \(\tan b = \frac{\text{opposite side}}{\text{adjacent side}}\).
The reciprocal of \(\tan b\) is the value you get when you flip the fraction, so it becomes \(\frac{\text{adjacent side}}{\text{opposite side}}\).
Recognize that the reciprocal of \(\tan b\) is the cotangent function, which is defined as \(\cot b = \frac{\text{adjacent side}}{\text{opposite side}}\).
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 \(\tan b\).
Therefore, the reciprocal of \(\tan b\) is \(\cot b\), which matches the correct answer.
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