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Chapter 10: Problem 16

Use your calculator to find each trigonometric ratio, correct to four decimal places. $$\cos 57.1^{\circ}$$

Short Answer

Expert verified
The cosine of 57.1 degrees is approximately 0.5446.

Step by step solution

01

Understand the Problem

The goal is to find the cosine of the angle 57.1 degrees and round it to four decimal places.
02

Set Calculator to Degree Mode

Ensure that the calculator is in degree mode because the angle is given in degrees. If it鈥檚 not, switch it to degree mode.
03

Enter the Angle

Enter 57.1 on the calculator.
04

Calculate the Cosine

Press the 'cos' button to calculate the cosine of 57.1 degrees.
05

Round to Four Decimal Places

Take the result and round it to four decimal places to get the final answer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

cosine function
The cosine function is a fundamental trigonometric ratio. It appears often in both pure and applied mathematics. When an angle is given, the cosine function helps in determining the ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle. For the angle \( \theta \), cosine is represented as \( \cos(\theta) \). For example, to find the cosine of 57.1 degrees, you follow these steps:
  • Ensure your calculator is in degree mode.
  • Enter the angle's value (57.1 degrees).
  • Press the 'cos' function to compute the value.
The resulting value will be a numeric representation of the cosine of the angle 57.1 degrees.
degree mode
In trigonometry, angles can be measured in degrees or radians. Usually, problems state which unit to use.
Most calculator issues stem from being in the wrong mode. Here, we need 'degree mode' because our angle (57.1 degrees) is provided in degrees.
To ensure your calculator is in degree mode, look for a mode button or setting.
Depending on your model, you might see 'DEG', 'D', or a degree symbol (掳). Adjust settings accordingly if you see 'RAD', indicating radian mode.
Keeping your calculator in the correct mode is crucial to getting the right results for trigonometric functions.
rounding decimal places
Rounding is crucial for obtaining manageable and practical results in mathematics. After computing the value of the trigonometric function, the result can span many decimal places.
However, the problem specifies rounding to four decimal places. Here鈥檚 a simple method:
  • First, look at the fifth decimal place.
  • If it's 5 or more, increase the fourth place by one.
  • If it's less than 5, leave the fourth place unchanged.
For example, if your result is 0.53726, you round it to 0.5373. This makes your answers precise yet easy to use.
calculator usage
Understanding how to effectively use your calculator can simplify solving trigonometric problems. Follow these steps to compute trigonometric ratios:
  • Turn on your calculator and ensure it is in the correct mode (degree mode for this angle).
  • Enter the value of the angle using the calculator keys (57.1).
  • Press the 'cos' button to calculate the cosine function of the entered angle.
  • Note the output result and round it to the necessary decimal places.
Using these steps routinely will make the calculation process faster and more accurate, minimizing errors.

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Most popular questions from this chapter

Devil's Tower is a rock formation. Jeremiah is standing 1200.0 feet from the base of the formation. The angle with the ground to the top of the rock is \(35.8^{\circ} .\) How high is the tower?

Solve each right triangle in Exercises \(1-18 .\) Remember that \(m \angle C=90^{\circ} .\) Round to the same number of decimal places as in the given information. $$b=7 \text { and } c=15$$

Use your calculator to find each trigonometric ratio, correct to four decimal places. $$\sin 12.4^{\circ}$$

Solve each right triangle in Exercises \(1-18 .\) Remember that \(m \angle C=90^{\circ} .\) Round to the same number of decimal places as in the given information. \(a=6\) and \(b=8\)

Use a calculator to find each ratio correct to four decimal places. $$\tan 81.43^{\circ}$$
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