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The tangent function, often written as \( \tan(x) \), is one of the fundamental functions in trigonometry. It can be understood as the ratio of the opposite side to the adjacent side in a right-angled triangle. The tangent function is particularly useful in many fields including engineering, physics, and astronomy.
If you're given an angle, say \( x \), and you’re asked to find the tangent of it, you're essentially finding how steep the angle is. The steeper the angle, the higher the value of \( \tan(x) \).
For example, in our problem, we were asked to find \( \tan(1.575) \). To further understand it:

• \( x \) should be in radians if it's not mentioned otherwise.
• Plug the value into the tangent function, usually by using a calculator.

Using a scientific calculator can make trigonometric calculations straightforward. Here are the steps to follow to find the tangent of a given angle using a scientific calculator:
First, make sure your calculator is in the right mode. For this problem, the angle is given in radians, so ensure your calculator is set to 'Radian' mode.
Then, input the angle: In this case, type in 1.575.
Lastly, press the tangent function key (usually labeled 'tan'). Your calculator should display the result, which is approximately 45.244 for \( \tan(1.575) \).
If your calculator is not in radians, the outcome will be incorrect. Always double-check your calculator settings before solving trigonometric functions.

Rounding numbers is a crucial skill in mathematics, especially when dealing with decimals. Here's how to round to the nearest tenth:

• First, identify the digit in the tenths place. In our example, 45.244, the tenths place is occupied by 2.
• Next, look at the digit in the hundredths place, which is 4 here.
• If this digit (4) is less than 5, you round down, leaving the tenths digit the same. If it were 5 or greater, you would round up.

Thus, 45.244 rounded to the nearest tenth is 45.2. Remember this method for all rounding tasks: focus on the digit immediately after the place you are rounding to, and apply the rounding rule.