To determine which trigonometric ratio has a value that is undefined, let's evaluate each option:
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cot(2): Cotangent is defined as the cosine of the angle divided by the sine of the angle. Since both sine and cosine are defined for any real number, cot(2) is defined.
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sec(3π/2): The secant function is the reciprocal of the cosine function. The cosine of \(3π/2\) is \(0\) (cos(3π/2) = 0), which makes sec(3π/2) undefined.
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tan(π): The tangent function is sine divided by cosine. Since sin(π) = 0 and cos(π) = -1, tan(π) = 0, which is defined.
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csc(π/2): The cosecant function is the reciprocal of sine. Since sin(π/2) = 1, csc(π/2) = 1, which is defined.
Based on the evaluations, the only trigonometric ratio that is undefined is:
sec(3π/2).
1 answer