Select The Correct Answer For Each Of The Following Statements.(i) $ 15^{\circ}\$} Is Equal To $[ \begin{tabular {ccccc} 225 & 150 & 1.5 & 1 & 0 \ A & B & C & D & E \ 25 & \sqrt{20} & 20 & \sqrt{10} & 5 \ A & B & C & D & E \ 28^4 &

Mar 13, 2025 by ADMIN 232 views

**Understanding Trigonometric Ratios and Angles**

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Introduction to Trigonometric Ratios

Trigonometric ratios are used to describe the relationships between the angles and side lengths of triangles. In this article, we will explore the concept of trigonometric ratios and how to select the correct answer for each of the following statements.

Understanding the Given Statements

The given statements involve trigonometric ratios and angles. We need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Trigonometric Ratios and Angles

Trigonometric ratios are used to describe the relationships between the angles and side lengths of triangles. The six basic trigonometric ratios are:

Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Cotangent (cot): The ratio of the length of the side adjacent to the angle to the length of the side opposite the angle.
Secant (sec): The ratio of the length of the hypotenuse to the length of the side adjacent to the angle.
Cosecant (csc): The ratio of the length of the hypotenuse to the length of the side opposite the angle.

Understanding the Given Options

The given options involve different values and trigonometric ratios. We need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Selecting the Correct Answer

To select the correct answer, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Understanding the Angle

The given angle is $15^{\circ}$ . We need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Understanding the Options

The given options involve different values and trigonometric ratios. We need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Applying Trigonometric Ratios

To apply trigonometric ratios, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Understanding the Trigonometric Ratios

The six basic trigonometric ratios are:

Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Cotangent (cot): The ratio of the length of the side adjacent to the angle to the length of the side opposite the angle.
Secant (sec): The ratio of the length of the hypotenuse to the length of the side adjacent to the angle.
Cosecant (csc): The ratio of the length of the hypotenuse to the length of the side opposite the angle.

Applying Trigonometric Ratios to the Given Angle

To apply trigonometric ratios to the given angle, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Solving the Given Problem

To solve the given problem, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Understanding the Given Options

The given options involve different values and trigonometric ratios. We need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Conclusion

In conclusion, to select the correct answer for each of the following statements, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Understanding the Trigonometric Ratios

The six basic trigonometric ratios are:

Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Cotangent (cot): The ratio of the length of the side adjacent to the angle to the length of the side opposite the angle.
Secant (sec): The ratio of the length of the hypotenuse to the length of the side adjacent to the angle.
Cosecant (csc): The ratio of the length of the hypotenuse to the length of the side opposite the angle.

Applying Trigonometric Ratios to the Given Angle

To apply trigonometric ratios to the given angle, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

Final Answer

The final answer is $\boxed{150}$ .

Explanation

The final answer is $\boxed{150}$ because the given angle is $15^{\circ}$ and the sine of $15^{\circ}$ is equal to $\frac{\sqrt{6}-\sqrt{2}}{4}$ , which is approximately equal to $0.2588$ . However, the given options do not include this value. The closest value to this value is $0.25$ , which is equal to $\frac{1}{4}$ . Therefore, the final answer is $\boxed{150}$ .

Conclusion

In conclusion, to select the correct answer for each of the following statements, we need to understand the concept of trigonometric ratios and how to apply them to solve the given problems.

References

[1] "Trigonometric Ratios." Wikipedia, Wikimedia Foundation, 12 Mar. 2023, en.wikipedia.org/wiki/Trigonometric_ratio.
[2] "Trigonometry." Khan Academy, Khan Academy, www.khanacademy.org/math/trigonometry.
[3] "Trigonometric Ratios." Math Open Reference, mathopenref.com/trig.html.

Note

The given options do not include the exact value of the sine of $15^{\circ}$ . However, the closest value to this value is $0.25$ , which is equal to $\frac{1}{4}$ . Therefore, the final answer is $\boxed{150}$ .

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Introduction

Q1: What are the six basic trigonometric ratios?

A1: The six basic trigonometric ratios are:

Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Cotangent (cot): The ratio of the length of the side adjacent to the angle to the length of the side opposite the angle.
Secant (sec): The ratio of the length of the hypotenuse to the length of the side adjacent to the angle.
Cosecant (csc): The ratio of the length of the hypotenuse to the length of the side opposite the angle.

Q2: How do I apply trigonometric ratios to solve problems?

A2: To apply trigonometric ratios to solve problems, you need to understand the concept of trigonometric ratios and how to apply them to solve the given problems. Here are the steps to follow:

Identify the given information, including the angle and the side lengths.
Determine the trigonometric ratio that is relevant to the problem.
Use the trigonometric ratio to set up an equation.
Solve the equation to find the unknown value.

Q3: What is the difference between sine and cosine?

A3: The sine and cosine are two of the six basic trigonometric ratios. The sine is the ratio of the length of the side opposite the angle to the length of the hypotenuse, while the cosine is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

Q4: How do I use trigonometric ratios to find the length of a side?

A4: To use trigonometric ratios to find the length of a side, you need to understand the concept of trigonometric ratios and how to apply them to solve the given problems. Here are the steps to follow:

Identify the given information, including the angle and the side lengths.
Determine the trigonometric ratio that is relevant to the problem.
Use the trigonometric ratio to set up an equation.
Solve the equation to find the unknown value.

Q5: What is the difference between tangent and cotangent?

A5: The tangent and cotangent are two of the six basic trigonometric ratios. The tangent is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle, while the cotangent is the ratio of the length of the side adjacent to the angle to the length of the side opposite the angle.

Q6: How do I use trigonometric ratios to find the measure of an angle?

A6: To use trigonometric ratios to find the measure of an angle, you need to understand the concept of trigonometric ratios and how to apply them to solve the given problems. Here are the steps to follow:

Identify the given information, including the side lengths and the trigonometric ratio.
Use the trigonometric ratio to set up an equation.
Solve the equation to find the measure of the angle.

Conclusion

In conclusion, trigonometric ratios are used to describe the relationships between the angles and side lengths of triangles. By understanding the concept of trigonometric ratios and how to apply them to solve problems, you can use trigonometric ratios to find the length of a side, the measure of an angle, and more.

References

[1] "Trigonometric Ratios." Wikipedia, Wikimedia Foundation, 12 Mar. 2023, en.wikipedia.org/wiki/Trigonometric_ratio.
[2] "Trigonometry." Khan Academy, Khan Academy, www.khanacademy.org/math/trigonometry.
[3] "Trigonometric Ratios." Math Open Reference, mathopenref.com/trig.html.

Note

The given information and the trigonometric ratios are used to solve the problems. By understanding the concept of trigonometric ratios and how to apply them to solve problems, you can use trigonometric ratios to find the length of a side, the measure of an angle, and more.