Using a Calculator to Find Trigonometry Values

Oct 13, 2025 by talynt.org 108 views

Introduction

In this article, we will be using a worked example as a guideline to complete a given table. The table involves solving trigonometry problems using a calculator and rounding off the answers to three decimal places where applicable. We will go through each step of the process and provide the necessary calculations to complete the table.

The Worked Example

Let's start by looking at the worked example given in the first row of the table.

Angle A	Angle B	Angle C	sin(A)	cos(A)	tan(A)
30°	60°	90°	0.5	0.866	0.577

In this example, we are given the angle A as 30° and we need to find the values of sin(A), cos(A), and tan(A). We can use a calculator to find these values.

Using a Calculator to Find Trigonometry Values

To find the values of sin(A), cos(A), and tan(A), we can use a calculator in degree mode. Here's how we can do it:

sin(A): To find the value of sin(A), we can use the sin function on the calculator. We enter the angle A as 30° and press the sin button. The calculator will display the value of sin(A) as 0.5.
cos(A): To find the value of cos(A), we can use the cos function on the calculator. We enter the angle A as 30° and press the cos button. The calculator will display the value of cos(A) as 0.866.
tan(A): To find the value of tan(A), we can use the tan function on the calculator. We enter the angle A as 30° and press the tan button. The calculator will display the value of tan(A) as 0.577.

Rounding Off Answers to Three Decimal Places

As mentioned earlier, we need to round off the answers to three decimal places where applicable. In this case, we need to round off the values of sin(A), cos(A), and tan(A) to three decimal places.

sin(A): The value of sin(A) is 0.5, which is already rounded off to three decimal places.
cos(A): The value of cos(A) is 0.866, which is already rounded off to three decimal places.
tan(A): The value of tan(A) is 0.577, which is already rounded off to three decimal places.

Completing the Table

Now that we have completed the first row of the table, we can use the same process to complete the rest of the table. We will use the same calculator and round off the answers to three decimal places where applicable.

Step 1: Find the Values of sin(A), cos(A), and tan(A)

To complete the table, we need to find the values of sin(A), cos(A), and tan(A) for each angle A. We can use a calculator to find these values.

Angle A	Angle B	Angle C	sin(A)	cos(A)	tan(A)
30°	60°	90°	0.5	0.866	0.577
45°	45°	90°	0.707	0.707	1
60°	30°	90°	0.866	0.5	1.732
90°	0°	90°	1	0	undefined

Step 2: Round Off Answers to Three Decimal Places

As mentioned earlier, we need to round off the answers to three decimal places where applicable. In this case, we need to round off the values of sin(A), cos(A), and tan(A) to three decimal places.

Angle A	Angle B	Angle C	sin(A)	cos(A)	tan(A)
30°	60°	90°	0.500	0.866	0.577
45°	45°	90°	0.707	0.707	1.000
60°	30°	90°	0.866	0.500	1.732
90°	0°	90°	1.000	0.000	undefined

Conclusion

In this article, we used a worked example as a guideline to complete a given table. We used a calculator to find the values of sin(A), cos(A), and tan(A) for each angle A and rounded off the answers to three decimal places where applicable. We completed the table by following the same process for each angle A.

Final Answer

The final answer is the completed table:

Angle A	Angle B	Angle C	sin(A)	cos(A)	tan(A)
30°	60°	90°	0.500	0.866	0.577
45°	45°	90°	0.707	0.707	1.000
60°	30°	90°	0.866	0.500	1.732
90°	0°	90°	1.000	0.000	undefined

Q: What is the purpose of the table in the previous article?

A: The purpose of the table is to provide a comprehensive list of trigonometry values for different angles. The table includes the values of sin(A), cos(A), and tan(A) for each angle A.

Q: How do I use a calculator to find trigonometry values?

A: To use a calculator to find trigonometry values, you need to enter the angle A in degree mode and press the corresponding trigonometry function button (sin, cos, or tan). The calculator will display the value of the trigonometry function.

Q: Why do I need to round off answers to three decimal places?

A: You need to round off answers to three decimal places to ensure accuracy and precision in your calculations. This is especially important when working with trigonometry values, as small errors can lead to significant differences in the final answer.

Q: Can I use a calculator to find trigonometry values for angles other than 30°, 45°, and 60°?

A: Yes, you can use a calculator to find trigonometry values for angles other than 30°, 45°, and 60°. Simply enter the angle A in degree mode and press the corresponding trigonometry function button (sin, cos, or tan).

Q: What happens if I enter an angle that is not in degree mode?

A: If you enter an angle that is not in degree mode, the calculator may display an error message or provide an incorrect answer. Make sure to enter the angle in degree mode to ensure accurate results.

Q: Can I use a calculator to find trigonometry values for angles greater than 90°?

A: Yes, you can use a calculator to find trigonometry values for angles greater than 90°. However, keep in mind that the values of sin(A) and cos(A) will be negative for angles greater than 90°.

Q: What is the difference between sin(A), cos(A), and tan(A)?

A: Sin(A), cos(A), and tan(A) are trigonometry functions that describe the relationships between the angles and sides of a right triangle. Sin(A) is the ratio of the opposite side to the hypotenuse, cos(A) is the ratio of the adjacent side to the hypotenuse, and tan(A) is the ratio of the opposite side to the adjacent side.

Q: Can I use a calculator to find trigonometry values for angles in radians?

A: Yes, you can use a calculator to find trigonometry values for angles in radians. However, you need to enter the angle in radian mode and press the corresponding trigonometry function button (sin, cos, or tan).

Q: What is the relationship between sin(A), cos(A), and tan(A)?

A: The relationship between sin(A), cos(A), and tan(A) is given by the following equations:

sin(A) = opposite side / hypotenuse
cos(A) = adjacent side / hypotenuse
tan(A) = opposite side / adjacent side

These equations describe the relationships between the angles and sides of a right triangle.

Conclusion

In this article, we have answered some of the most frequently asked questions about trigonometry and the use of calculators to find trigonometry values. We have also discussed the relationships between sin(A), cos(A), and tan(A) and provided examples of how to use a calculator to find trigonometry values for different angles.