If `x=1.75` radians, then the value of cosx is closet in value of which of the following?

Options

A. `-cos1.39`
B. `cos4.89`
C. `cos4.53`
D. `-cos0.18`

Answer

To solve the question, we need to find the value of \( \cos(1.75) \) radians and compare it with the cosine values of the other angles provided. Here’s a step-by-step solution:

### Step 1: Calculate \( \cos(1.75) \)
Using a scientific calculator or a cosine table, we find:
\[ \cos(1.75) \approx -0.178 \]

### Step 2: Calculate the cosine values of the other angles
Now, we will calculate the cosine for the other angles provided in the question:

1. **Calculate \( \cos(1.39) \)**
\[ \cos(1.39) \approx 0.173 \]
Thus, \( -\cos(1.39) \approx -0.173 \).

2. **Calculate \( \cos(4.89) \)**
\[ \cos(4.89) \approx 0.176 \]

3. **Calculate \( \cos(4.53) \)**
\[ \cos(4.53) \approx -0.181 \]

4. **Calculate \( \cos(0.18) \)**
\[ \cos(0.18) \approx 0.983 \]
Thus, \( -\cos(0.18) \approx -0.983 \).

### Step 3: Compare the values
Now we have the following values:
- \( \cos(1.75) \approx -0.178 \)
- \( -\cos(1.39) \approx -0.173 \)
- \( \cos(4.89) \approx 0.176 \)
- \( \cos(4.53) \approx -0.181 \)
- \( -\cos(0.18) \approx -0.983 \)

### Step 4: Determine the closest value
Now we compare these values to find which one is closest to \( -0.178 \):
- The value \( -0.173 \) (from \( -\cos(1.39) \)) is closer to \( -0.178 \) than the other values.

### Conclusion
Thus, the value of \( \cos(1.75) \) is closest to \( -\cos(1.39) \).

### Final Answer
The answer is \( -\cos(1.39) \).

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