Use Your Calculator To Find The Angle, To The Nearest Hundredth Of A Degree, Whose Sine Value Is $\frac{1}{3}$.A. $0.33^{\circ}$ B. $0.34^{\circ}$ C. $70.53^{\circ}$ D. $19.47^{\circ}$

Introduction

In trigonometry, the sine function is a fundamental concept used to describe the relationship between the angles and side lengths of triangles. Given a specific sine value, we can use a calculator to find the corresponding angle. In this article, we will explore how to use a calculator to find the angle whose sine value is $\frac{1}{3}$, rounded to the nearest hundredth of a degree.

Understanding the Sine Function

The sine function is a periodic function that oscillates between -1 and 1. It is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angled triangle. The sine function is denoted by the symbol $\sin(x)$, where $x$ is the angle in radians or degrees.

Using a Calculator to Find the Angle

To find the angle whose sine value is $\frac{1}{3}$, we can use a calculator in radian mode. First, we need to enter the sine function and the value $\frac{1}{3}$ into the calculator. The calculator will then display the angle in radians.

Step 1: Enter the Sine Function and Value

• Press the SIN button on the calculator to enter the sine function.
• Enter the value $\frac{1}{3}$ by pressing the 1 button, followed by the / button, and then the 3 button.
• Press the ENTER button to execute the function.

Step 2: Convert the Angle to Degrees

The calculator will display the angle in radians. To convert the angle to degrees, we need to multiply the angle in radians by $\frac{180}{\pi}$.

Step 3: Round the Angle to the Nearest Hundredth of a Degree

Once we have the angle in degrees, we need to round it to the nearest hundredth of a degree. This can be done by using the ROUND function on the calculator.

Calculating the Angle

Let's calculate the angle whose sine value is $\frac{1}{3}$ using a calculator.

• Enter the sine function and value into the calculator: SIN(1/3)
• Press the ENTER button to execute the function: 0.3333333333333333
• Convert the angle to degrees: 0.3333333333333333 \* (180/π) = 19.47122063485758
• Round the angle to the nearest hundredth of a degree: 19.47

Conclusion

In this article, we used a calculator to find the angle whose sine value is $\frac{1}{3}$. We entered the sine function and value into the calculator, converted the angle to degrees, and rounded it to the nearest hundredth of a degree. The correct answer is 19.47^{\circ}.

Discussion

• What is the sine function, and how is it used in trigonometry?
• How do you use a calculator to find the angle whose sine value is given?
• What is the difference between radians and degrees, and how do you convert between them?

Answer Key

Q: What is the sine function, and how is it used in trigonometry?

A: The sine function is a fundamental concept in trigonometry that describes the relationship between the angles and side lengths of triangles. It is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angled triangle. The sine function is denoted by the symbol $\sin(x)$, where $x$ is the angle in radians or degrees.

Q: How do you use a calculator to find the angle whose sine value is given?

A: To find the angle whose sine value is given, you can use a calculator in radian mode. First, enter the sine function and the value into the calculator. Then, press the ENTER button to execute the function. The calculator will display the angle in radians. To convert the angle to degrees, multiply the angle in radians by $\frac{180}{\pi}$.

Q: What is the difference between radians and degrees, and how do you convert between them?

A: Radians and degrees are two different units of measurement for angles. Radians are a more fundamental unit of measurement, and degrees are a derived unit. To convert radians to degrees, multiply the angle in radians by $\frac{180}{\pi}$. To convert degrees to radians, multiply the angle in degrees by $\frac{\pi}{180}$.

Q: How do you round an angle to the nearest hundredth of a degree?

A: To round an angle to the nearest hundredth of a degree, use the ROUND function on the calculator. This function will round the angle to the nearest hundredth of a degree.

Q: What is the correct answer to the problem of finding the angle whose sine value is $\frac{1}{3}$?

A: The correct answer to the problem of finding the angle whose sine value is $\frac{1}{3}$ is $19.47^{\circ}$.

Q: Can you use a calculator to find the angle whose sine value is a decimal value?

A: Yes, you can use a calculator to find the angle whose sine value is a decimal value. Simply enter the sine function and the decimal value into the calculator, and press the ENTER button to execute the function.

Q: How do you use a calculator to find the angle whose sine value is a fraction?

A: To use a calculator to find the angle whose sine value is a fraction, first convert the fraction to a decimal value. Then, enter the sine function and the decimal value into the calculator, and press the ENTER button to execute the function.

Q: Can you use a calculator to find the angle whose sine value is a negative value?

A: Yes, you can use a calculator to find the angle whose sine value is a negative value. Simply enter the sine function and the negative value into the calculator, and press the ENTER button to execute the function.

Q: How do you use a calculator to find the angle whose sine value is a complex value?

A: To use a calculator to find the angle whose sine value is a complex value, first convert the complex value to a decimal value. Then, enter the sine function and the decimal value into the calculator, and press the ENTER button to execute the function.

Conclusion

In this article, we have answered some frequently asked questions about using a calculator to find the angle whose sine value is given. We have covered topics such as the sine function, radians and degrees, rounding angles, and using a calculator to find angles with decimal, fraction, negative, and complex values.