Calculate The Length BC. A Sin ⁡ ( 115 ° ) = 7 C M Sin ⁡ ( 30 ° ) { \frac{a}{\sin(115°)} = \frac{7cm}{\sin(30°)} } S I N ( 115° ) A ​ = S I N ( 30° ) 7 C M ​ BC = Cm [4]

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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 that has numerous applications in various fields, including physics, engineering, and navigation. In this article, we will focus on solving trigonometric equations, specifically the equation involving the sine function.

Understanding the Equation

The given equation is:

asin⁡(115°)=7cmsin⁡(30°){ \frac{a}{\sin(115°)} = \frac{7cm}{\sin(30°)} }

Our goal is to solve for the length of BC, denoted by 'a'. To do this, we need to isolate 'a' on one side of the equation.

Step 1: Simplify the Equation

The first step is to simplify the equation by eliminating the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is sin(115°)sin(30°).

\frac{a}{\sin(115°)} = \frac{7cm}{\sin(30°)}

Multiplying both sides by sin(115°)sin(30°):

a \cdot \sin(30°) = 7cm \cdot \sin(115°)

Step 2: Evaluate the Sine Functions

Next, we need to evaluate the sine functions on both sides of the equation. We can use a calculator or a trigonometric table to find the values of sin(30°) and sin(115°).

\sin(30°) = 0.5
\sin(115°) = 0.96

Substituting these values into the equation:

a \cdot 0.5 = 7cm \cdot 0.96

Step 3: Solve for 'a'

Now, we can solve for 'a' by dividing both sides of the equation by 0.5.

a = \frac{7cm \cdot 0.96}{0.5}

Simplifying the expression:

a = 13.44cm

Conclusion

In this article, we solved a trigonometric equation involving the sine function. We simplified the equation, evaluated the sine functions, and solved for the length of BC. The final answer is:

BC = 13.44cm

Tips and Tricks

  • When solving trigonometric equations, it's essential to simplify the equation by eliminating fractions.
  • Use a calculator or a trigonometric table to evaluate the sine functions.
  • Make sure to isolate the variable on one side of the equation.

Frequently Asked Questions

  • Q: What is the formula for solving trigonometric equations? A: The formula for solving trigonometric equations involves simplifying the equation, evaluating the sine functions, and solving for the variable.
  • Q: How do I simplify a trigonometric equation? A: To simplify a trigonometric equation, eliminate fractions by multiplying both sides by the least common multiple (LCM) of the denominators.
  • Q: What is the value of sin(115°)? A: The value sin(115°) is approximately 0.96.
    Trigonometry Q&A: Frequently Asked Questions and Answers ===========================================================

Introduction

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental subject that has numerous applications in various fields, including physics, engineering, and navigation. In this article, we will answer some of the most frequently asked questions about trigonometry.

Q&A

Q: What is trigonometry?

A: Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Q: What are the basic trigonometric functions?

A: The basic trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles of a triangle to the ratios of the lengths of its sides.

Q: What is the sine function?

A: The sine function is a trigonometric function that relates the angle of a triangle to the ratio of the length of the opposite side to the length of the hypotenuse.

Q: What is the cosine function?

A: The cosine function is a trigonometric function that relates the angle of a triangle to the ratio of the length of the adjacent side to the length of the hypotenuse.

Q: What is the tangent function?

A: The tangent function is a trigonometric function that relates the angle of a triangle to the ratio of the length of the opposite side to the length of the adjacent side.

Q: How do I solve a trigonometric equation?

A: To solve a trigonometric equation, simplify the equation by eliminating fractions, evaluate the trigonometric functions, and solve for the variable.

Q: What is the formula for solving trigonometric equations?

A: The formula for solving trigonometric equations involves simplifying the equation, evaluating the trigonometric functions, and solving for the variable.

Q: How do I simplify a trigonometric equation?

A: To simplify a trigonometric equation, eliminate fractions by multiplying both sides by the least common multiple (LCM) of the denominators.

Q: What is the value of sin(30°)?

A: The value of sin(30°) is 0.5.

Q: What is the value of cos(45°)?

A: The value of cos(45°) is 0.707.

Q: What is the value of tan(60°)?

A: The value of tan(60°) is 1.732.

Q: How do I use trigonometry in real-life situations?

A: Trigonometry is used in various real-life situations, including navigation, physics, engineering, and architecture. It is used to calculate distances, heights, and angles in these fields.

Q: What are some common trigonometric identities?

A: Some common trigonometric identities include the Pythagorean identity (sin^2(x) + cos^2(x) = 1), the sum and difference formulas (sin(x+y) = sin(x)cos(y) + cos(x)sin(y)), and the double-angle formulas (sin(2x) = 2sin(x)cos(x)).

Q: How do I memorize trigonometric identities?

A: To memorize trigonometric identities, practice using them in different problems and exercises. You can also use flashcards or create a concept map to help you remember the identities.

Conclusion

In this article, we answered some of the most frequently asked questions about trigonometry. We covered the basic trigonometric functions, the sine, cosine, and tangent functions, and how to solve trigonometric equations. We also discussed some common trigonometric identities and how to memorize them. We hope this article has been helpful in answering your questions about trigonometry.

Tips and Tricks

  • Practice using trigonometric identities in different problems and exercises.
  • Use flashcards or create a concept map to help you remember the identities.
  • Review the basic trigonometric functions and their relationships to the sides and angles of triangles.
  • Use a calculator or a trigonometric table to evaluate the sine, cosine, and tangent functions.

Frequently Asked Questions

  • Q: What is the formula for solving trigonometric equations? A: The formula for solving trigonometric equations involves simplifying the equation, evaluating the trigonometric functions, and solving for the variable.
  • Q: How do I simplify a trigonometric equation? A: To simplify a trigonometric equation, eliminate fractions by multiplying both sides by the least common multiple (LCM) of the denominators.
  • Q: What is the value of sin(30°)? A: The value of sin(30°) is 0.5.