1. Convert 95 inches to feet. Round to the nearest tenth of a foot. Recall 12 inches =1 foot. feet Question Help: Message instructor Submit Question Jump to Answer Question 3
2. Evaluate arctan(0)
The Correct Answer and Explanation is :
1. Convert 95 inches to feet
To convert inches to feet, we use the conversion factor that 12 inches equals 1 foot. So to convert 95 inches to feet:
[
\text{Feet} = \frac{\text{Inches}}{12} = \frac{95}{12} \approx 7.9 \text{ feet}
]
So, 95 inches is approximately 7.9 feet (rounded to the nearest tenth).
2. Evaluate arctan(0)
The arctangent (or inverse tangent) of a number is the angle whose tangent is that number. In this case, we are asked to evaluate:
[
\text{arctan}(0)
]
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the adjacent side. Therefore, when the tangent of an angle is 0, it means the opposite side is 0, and thus the angle must be 0 degrees or 0 radians.
[
\text{arctan}(0) = 0
]
This result holds in both degrees and radians:
- In radians, (\text{arctan}(0) = 0 \text{ radians}).
- In degrees, (\text{arctan}(0) = 0^\circ).
Explanation
The arctangent function, also known as the inverse tangent, is commonly used in trigonometry to find the angle given a tangent value. Its domain is all real numbers, and its range typically lies within the interval ((- \frac{\pi}{2}, \frac{\pi}{2})) or equivalently ((-90^\circ, 90^\circ)), depending on whether the result is in radians or degrees.
When evaluating (\text{arctan}(x)), the result is the angle whose tangent is equal to (x). For example:
- (\text{arctan}(1)) results in an angle of 45° or (\frac{\pi}{4}) radians.
- (\text{arctan}(\infty)) gives 90° or (\frac{\pi}{2}) radians because the tangent of 90° approaches infinity.
Since (\text{tan}(0) = 0), it follows that (\text{arctan}(0) = 0). This means the angle whose tangent is zero is 0 degrees (or 0 radians), confirming that arctan(0) evaluates to 0.