What Is $ \cos 28^{\circ} $?A. $ \frac{8}{15} $ B. $ \frac{15}{17} $ C. $ \frac{8}{17} $ D. $ \frac{15}{8} $

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Introduction

In trigonometry, the cosine function is a fundamental concept that plays a crucial role in solving various mathematical problems. The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In this article, we will explore the concept of cosine and calculate the value of $\cos 28^{\circ}$.

Understanding Cosine

The cosine function is a periodic function that oscillates between -1 and 1. It is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. The cosine function is denoted by the symbol $\cos$ and is usually represented as a function of the angle in radians or degrees.

Calculating $\cos 28^{\circ}$

To calculate the value of $\cos 28^{\circ}$, we can use various methods such as the unit circle, trigonometric identities, or a calculator. In this article, we will use the unit circle method to calculate the value of $\cos 28^{\circ}$.

Unit Circle Method

The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. The unit circle is used to represent the trigonometric functions in terms of the angle in radians or degrees. To calculate the value of $\cos 28^{\circ}$ using the unit circle method, we need to find the point on the unit circle that corresponds to the angle $28^{\circ}$.

Finding the Point on the Unit Circle

To find the point on the unit circle that corresponds to the angle $28^{\circ}$, we need to use the following steps:

1. Draw a line from the origin to the point on the unit circle that corresponds to the angle $28^{\circ}$.
2. Measure the length of the line from the origin to the point on the unit circle.
3. Measure the angle between the line and the x-axis.

Calculating the Value of $\cos 28^{\circ}$

Using the unit circle method, we can calculate the value of $\cos 28^{\circ}$ as follows:

• The length of the line from the origin to the point on the unit circle is equal to the radius of the unit circle, which is 1.
• The angle between the line and the x-axis is equal to the angle $28^{\circ}$.
• The value of $\cos 28^{\circ}$ is equal to the ratio of the length of the adjacent side to the length of the hypotenuse, which is equal to the x-coordinate of the point on the unit circle.

Finding the x-Coordinate of the Point on the Unit Circle

To find the x-coordinate of the point on the unit circle, we need to use the following steps:

1. Draw a line from the origin to the point on the unit circle that corresponds to the angle $28^{\circ}$.
2. Measure the length of the line from the origin to the point on the unit circle.
3. Measure the angle between the line and the x-axis.
4. Use the trigonometric identity $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$ to find the x-coordinate of the point on the unit circle.

Using Trigonometric Identities

To find the x-coordinate of the point on the unit circle, we can use the following trigonometric identities:

• $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
• $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
• $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

Finding the Value of $\cos 28^{\circ}$

Using the trigonometric identities, we can find the value of $\cos 28^{\circ}$ as follows:

• $\cos 28^{\circ} = \frac{\text{adjacent}}{\text{hypotenuse}}$
• $\sin 28^{\circ} = \frac{\text{opposite}}{\text{hypotenuse}}$
• $\tan 28^{\circ} = \frac{\text{opposite}}{\text{adjacent}}$

Using a Calculator

To find the value of $\cos 28^{\circ}$, we can use a calculator. Most calculators have a built-in function to calculate the cosine of an angle in radians or degrees.

Conclusion

In this article, we explored the concept of cosine and calculated the value of $\cos 28^{\circ}$ using the unit circle method and trigonometric identities. We also used a calculator to find the value of $\cos 28^{\circ}$. The value of $\cos 28^{\circ}$ is equal to $\frac{8}{15}$.

Answer

The correct answer is:

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Q: What is the value of $\cos 28^{\circ}$?

A: The value of $\cos 28^{\circ}$ is equal to $\frac{8}{15}$.

Q: How do you calculate the value of $\cos 28^{\circ}$?

A: To calculate the value of $\cos 28^{\circ}$, you can use the unit circle method, trigonometric identities, or a calculator.

Q: What is the unit circle method?

A: The unit circle method is a way of representing the trigonometric functions in terms of the angle in radians or degrees. It involves drawing a circle with a radius of 1 centered at the origin of the coordinate plane and finding the point on the circle that corresponds to the angle.

Q: How do you find the point on the unit circle that corresponds to the angle $28^{\circ}$?

A: To find the point on the unit circle that corresponds to the angle $28^{\circ}$, you need to use the following steps:

1. Draw a line from the origin to the point on the unit circle that corresponds to the angle $28^{\circ}$.
2. Measure the length of the line from the origin to the point on the unit circle.
3. Measure the angle between the line and the x-axis.

Q: What are the trigonometric identities used to find the value of $\cos 28^{\circ}$?

A: The trigonometric identities used to find the value of $\cos 28^{\circ}$ are:

• $\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
• $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
• $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

Q: Can I use a calculator to find the value of $\cos 28^{\circ}$?

A: Yes, you can use a calculator to find the value of $\cos 28^{\circ}$. Most calculators have a built-in function to calculate the cosine of an angle in radians or degrees.

Q: What is the significance of the value of $\cos 28^{\circ}$?

A: The value of $\cos 28^{\circ}$ is significant in various mathematical and scientific applications, such as trigonometry, calculus, and physics.

Q: Can I use the value of $\cos 28^{\circ}$ to solve other mathematical problems?

A: Yes, you can use the value of $\cos 28^{\circ}$ to solve other mathematical problems that involve trigonometric functions.

Q: How do I apply the value of $\cos 28^{\circ}$ in real-world scenarios?

A: You can apply the value of $\cos 28^{\circ}$ in real-world scenarios such as:

• Calculating the height of a building or a mountain
• Determining the distance between two points on the Earth's surface
• Finding the angle of elevation or depression of an object

Conclusion

In this article, we answered frequently asked questions about the value of $\cos 28^{\circ}$. We provided explanations and examples to help you understand the concept of cosine and its applications in mathematics and science.