cot(\frac{\pi}{2})=
A. 0
B. Undefined
C. -1
D. 1
Answer (2)
The problem asks to find the value of cot ( 2 π ) .
Recall that cot ( x ) = s i n ( x ) c o s ( x ) .
Evaluate cos ( 2 π ) = 0 and sin ( 2 π ) = 1 .
Calculate cot ( 2 π ) = 1 0 = 0 , so the answer is 0 .
Explanation
Understanding the Problem We are asked to find the value of the cotangent function at 2 π . The cotangent function is defined as cot ( x ) = s i n ( x ) c o s ( x ) .
Evaluating Sine and Cosine We need to evaluate cos ( 2 π ) and sin ( 2 π ) . From the unit circle or trigonometric knowledge, we know that cos ( 2 π ) = 0 and sin ( 2 π ) = 1 .
Calculating Cotangent Now, we substitute these values into the expression for the cotangent function: cot ( 2 π ) = sin ( 2 π ) cos ( 2 π ) = 1 0 = 0.
Final Answer Therefore, the value of cot ( 2 π ) is 0. Comparing this result with the given options, we find that the correct answer is A.
Examples
Cotangent is used in various fields like physics and engineering to describe angles and slopes. For example, when analyzing the stability of a ladder leaning against a wall, the cotangent of the angle between the ladder and the ground helps determine the ladder's stability. If the angle is 2 π (90 degrees), the ladder is vertical, and cot ( 2 π ) = 0 , indicating a special case where the ladder is perfectly upright and doesn't exert a horizontal force on the wall.
The value of cot ( 2 π ) is 0 , as calculated using the cotangent function definition. Thus, the correct answer is A. Understanding the sine and cosine relationships at this angle is key to finding the result.
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