Calculating Trigonometric Ratios Using a Calculator

Oct 13, 2025 by talynt.org 11 views

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Introduction

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental subject in mathematics and has numerous applications in various fields, including physics, engineering, and navigation. In this article, we will focus on calculating trigonometric ratios using a calculator, specifically the tangent function.

What is the Tangent Function?

The tangent function is a fundamental trigonometric function that is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle in a right-angled triangle. It is denoted by the symbol tan and is calculated as:

tan(θ) = opposite side / adjacent side

where θ is the angle in question.

Calculating Trigonometric Ratios Using a Calculator

To calculate trigonometric ratios using a calculator, we need to use the inverse tangent function, which is denoted by the symbol tan^(-1) or arctan. This function returns the angle whose tangent is a given number.

Calculating tan(15°)

To calculate tan(15°), we can use a calculator and enter the following values:

Angle: 15°
Function: tan
Mode: degrees

Using a calculator, we get:

tan(15°) = 0.2679

Calculating tan(64°)

To calculate tan(64°), we can use a calculator and enter the following values:

Angle: 64°
Function: tan
Mode: degrees

Using a calculator, we get:

tan(64°) = 2.1455

Calculating tan(20°)

To calculate tan(20°), we can use a calculator and enter the following values:

Angle: 20°
Function: tan
Mode: degrees

Using a calculator, we get:

tan(20°) = 0.3640

Calculating tan(90°)

To calculate tan(90°), we can use a calculator and enter the following values:

Angle: 90°
Function: tan
Mode: degrees

Using a calculator, we get:

tan(90°) = undefined

Discussion

In this article, we have calculated the values of four trigonometric ratios using a calculator. We have used the inverse tangent function to find the angles whose tangents are given numbers. The results show that the tangent function is a powerful tool for solving trigonometric problems.

Conclusion

In conclusion, calculating trigonometric ratios using a calculator is a straightforward process that can be accomplished using the inverse tangent function. By following the steps outlined in this article, we can easily calculate the values of trigonometric ratios and solve a wide range of problems in mathematics and other fields.

References

[1] "Trigonometry" by Michael Corral, 2019.
[2] "Calculus" by Michael Spivak, 2008.
[3] "Trigonometry for Dummies" by Mary Jane Sterling, 2018.

Future Work

In future work, we plan to explore other trigonometric functions, such as the sine and cosine functions, and calculate their values using a calculator. We also plan to apply trigonometry to real-world problems, such as navigation and physics.

Glossary

Tangent function: a trigonometric function that is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle in a right-angled triangle.
Inverse tangent function: a function that returns the angle whose tangent is a given number.
Right-angled triangle: a triangle with one angle equal to 90°.
Trigonometry: a branch of mathematics that deals with the relationships between the sides and angles of triangles.

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Introduction

In our previous article, we discussed how to calculate trigonometric ratios using a calculator. We covered the basics of the tangent function and how to use the inverse tangent function to find the angles whose tangents are given numbers. In this article, we will answer some frequently asked questions about calculating trigonometric ratios using a calculator.

Q&A

Q: What is the difference between the tangent function and the inverse tangent function?

A: The tangent function is a trigonometric function that is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle in a right-angled triangle. The inverse tangent function, on the other hand, is a function that returns the angle whose tangent is a given number.

Q: How do I enter the angle in degrees on my calculator?

A: To enter the angle in degrees on your calculator, you need to make sure that the calculator is set to degree mode. This is usually done by pressing the "MODE" button and selecting "DEG" from the menu. Once you have selected degree mode, you can enter the angle in degrees using the number keys.

Q: Can I use a calculator to calculate trigonometric ratios for angles greater than 90°?

A: Yes, you can use a calculator to calculate trigonometric ratios for angles greater than 90°. However, you need to make sure that the calculator is set to degree mode and that the angle is entered in degrees.

Q: What is the range of the tangent function?

A: The range of the tangent function is all real numbers. This means that the tangent function can take on any value, positive or negative, and that there is no upper or lower limit to the values that the tangent function can take.

Q: Can I use a calculator to calculate trigonometric ratios for angles that are not in degrees?

A: Yes, you can use a calculator to calculate trigonometric ratios for angles that are not in degrees. However, you need to make sure that the calculator is set to the correct mode (e.g. radians or degrees) and that the angle is entered in the correct units.

Q: How do I calculate the value of the tangent function for a given angle using a calculator?

A: To calculate the value of the tangent function for a given angle using a calculator, you need to enter the angle in the correct mode (e.g. degrees or radians) and then press the "TAN" button. The calculator will then display the value of the tangent function for the given angle.

Conclusion

In this article, we have answered some frequently asked questions about calculating trigonometric ratios using a calculator. We have covered topics such as the difference between the tangent function and the inverse tangent function, how to enter the angle in degrees on a calculator, and how to calculate the value of the tangent function for a given angle using a calculator.

References

[1] "Trigonometry" by Michael Corral, 2019.
[2] "Calculus" by Michael Spivak, 2008.
[3] "Trigonometry for Dummies" by Mary Jane Sterling, 2018.

Future Work

Glossary

Tangent function: a trigonometric function that is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle in a right-angled triangle.
Inverse tangent function: a function that returns the angle whose tangent is a given number.
Right-angled triangle: a triangle with one angle equal to 90°.
Trigonometry: a branch of mathematics that deals with the relationships between the sides and angles of triangles.