Problem 35 - Precalculus : Building Concepts and Connections

Question

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. $$\sin 38^{\circ}$$

Step-by-Step Solution

Answer

The exact value will depend on your calculator but should be approximately 0.6157 when rounded to four decimal places.

Step 1: Set Calculator to DEGREE mode

First, ensure that the calculator is in DEGREE mode. This is crucial as the given value is in degrees, and the calculator's mode will affect the output values. Generally, you can find this setting under the mode or settings option in the calculator.

Step 2: Input the Function

Next, input the function \(\sin 38^{\circ}\) into the calculator. This can usually be done by first pressing the 'sin' button, followed by the number 38.

Step 3: Evaluation and Rounding

Evaluate the function using the calculator and the result will be displayed. Ensure the final answer is rounded to four decimal places as per the exercise instructions.

Key Concepts

Scientific Calculator Usage

Using a scientific calculator can seem daunting, but it's a reliable tool for students to evaluate complex mathematical functions, including trigonometric ones. When you're presented with a problem like evaluating \( \sin 38^\circ \), a scientific calculator is indispensable.

To start, familiarize yourself with the calculator's layout. Look for the 'sin' button, which is often in a section grouped with other trigonometric functions like 'cos' and 'tan'. Keying this function into the calculator involves a clear sequence: press the 'sin' button followed by the numerical value you are evaluating—in this case, 38.
Remember that most scientific calculators have multifunctional buttons, which means you might need to press a 'shift' or '2nd' key to access the sine function. It's crucial to ensure you're inputting the exact function and value you need for the calculation to get the correct answer.

Degree Mode

One essential aspect of evaluating trigonometric functions is ensuring that your scientific calculator is set to the correct mode: Degree or Radian. Since the exercise requires evaluating \( \sin 38^\circ \), you must use Degree mode.

Different calculators have different ways of switching between modes. Here’s what you generally do: locate the button that allows you to change modes—this may be labelled as 'Mode,' 'Deg/Rad,' or similar. Upon selecting it, choose the option that sets the calculator to Degree mode. This is absolutely crucial because using Radian mode for degree measurements will give you incorrect results.
It's a good tip to double-check the mode before starting your calculations. Many calculators feature a small indicator on the display that shows what mode you're in, so make sure you see an indication that you're in Degree mode.

Rounding Decimal Places

Upon obtaining the result from your scientific calculator, the next step is rounding to the required number of decimal places. The instructions specify rounding to four decimal places.

Rounding is an important skill in mathematics to express a number more concisely or to match a specified precision. When the calculator presents the result, identify the fifth decimal place. If this digit is 5 or greater, you'll increase the fourth decimal by one. If it's less than 5, leave the fourth decimal as is and drop all the following digits.
For example, if your calculator shows 0.61547 for \( \sin 38^\circ \), you would round this to 0.6155 since the fifth decimal is 7. It's good practice to ensure consistency in the number of decimals throughout your work, as it can be crucial in communicating the precision of your calculations.