Question
Which trigonometric function has a range that does not include 0.4?
(1 point)
Responses
y = cos x
y = cos x
y = cot x
y = cot x
y = csc x
y = csc x
y = sin x
(1 point)
Responses
y = cos x
y = cos x
y = cot x
y = cot x
y = csc x
y = csc x
y = sin x
Answers
GPT-4o mini
To determine which trigonometric function has a range that does not include 0.4, let's analyze the ranges of the given functions:
1. **y = cos x**: The range of the cosine function is [-1, 1]. Therefore, it does include 0.4.
2. **y = cot x**: The cotangent function can take on all real values, so it does include 0.4.
3. **y = csc x**: The cosecant function, which is the reciprocal of the sine function, has a range of (-∞, -1] ∪ [1, ∞). Therefore, it does not include values between -1 and 1, including 0.4.
4. **y = sin x**: The range of the sine function is [-1, 1]. Therefore, it does include 0.4.
Based on this analysis, the trigonometric function whose range does not include 0.4 is:
**y = csc x**.
1. **y = cos x**: The range of the cosine function is [-1, 1]. Therefore, it does include 0.4.
2. **y = cot x**: The cotangent function can take on all real values, so it does include 0.4.
3. **y = csc x**: The cosecant function, which is the reciprocal of the sine function, has a range of (-∞, -1] ∪ [1, ∞). Therefore, it does not include values between -1 and 1, including 0.4.
4. **y = sin x**: The range of the sine function is [-1, 1]. Therefore, it does include 0.4.
Based on this analysis, the trigonometric function whose range does not include 0.4 is:
**y = csc x**.