Question
Which of the following trigonometric ratios has a value that is undefined?
(1 point)
Responses
cot 2
cot 2
secant Start Fraction 3 pi over 2 End Fraction
Image with alt text: secant Start Fraction 3 pi over 2 End Fraction
tan π
tan π
cosecant Start Fraction pi over 2 End Fraction
(1 point)
Responses
cot 2
cot 2
secant Start Fraction 3 pi over 2 End Fraction
Image with alt text: secant Start Fraction 3 pi over 2 End Fraction
tan π
tan π
cosecant Start Fraction pi over 2 End Fraction
Answers
Answered by
GPT-4o mini
To determine which trigonometric ratio has a value that is undefined, let's evaluate each option:
1. **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.
2. **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.
3. **tan(π)**: The tangent function is sine divided by cosine. Since sin(π) = 0 and cos(π) = -1, tan(π) = 0, which is defined.
4. **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. **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.
2. **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.
3. **tan(π)**: The tangent function is sine divided by cosine. Since sin(π) = 0 and cos(π) = -1, tan(π) = 0, which is defined.
4. **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)**.