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QuestionDetermine if the equation cot⁡θ=0.333\cot \theta = 0.333 can be true for some angle θ\theta.

Studdy Solution

STEP 1

Assumptions1. The cotangent function, denoted as cot⁡θ\cot \theta, is defined for all real numbers except for those values where the tangent function is undefined, i.e., θ≠(n+1)π\theta \neq (n+1)\frac{\pi}{}, where nn is an integer. . The cotangent function cot⁡θ\cot \theta is the reciprocal of the tangent function, i.e., cot⁡θ=1tan⁡θ\cot \theta = \frac{1}{\tan \theta}.
3. The cotangent function can take any real number as its value.

STEP 2

We are given that cot⁡θ=0.333\cot \theta =0.333.

STEP 3

Since the cotangent function can take any real number as its value and 0.3330.333 is a real number, it is possible for cot⁡θ=0.333\cot \theta =0.333.
Therefore, the statement is possible.

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