Solve for x using trigonometric ratios

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In summary, the conversation discusses finding the value of x in a mathematical term of the form tan(A.x)/tan(B.x)=C. One approach suggested is using the addition theorem for sine, while another is solving it numerically with help from WolframAlpha.com. Additionally, the use of the addition theorem leads to the equation sin(A+B)x=-sin(A-B)x, which can be solved by using -sin(α)=sin(-α) and applying arcsin.
  • #1
Sourav Guha
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I have a mathematical term of the form tan(A.x)/tan(B.x)=C.How do I find out the value of x?
 
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  • #2
I would try the addition theorem for sine, since you have ##\sin(Ax) \cos(Bx) = C \sin(Bx) \cos(Cx)##. Or solve it numerically, e.g. by the help of WolframAlpha.com.
 
  • #3
fresh_42 said:
I would try the addition theorem for sine, since you have ##\sin(Ax) \cos(Bx) = C \sin(Bx) \cos(Cx)##. Or solve it numerically, e.g. by the help of WolframAlpha.com.
By using Addition Theorem,I finally get sin(A+B)x=-sin(A-B)x..Now how do I find x?
 
  • #4
Sourav Guha said:
By using Addition Theorem,I finally get sin(A+B)x=-sin(A-B)x..Now how do I find x?
I wonder where the ##C## has gone. But if you have what you say, then we can use ##-\sin(\alpha)=\sin(-\alpha)## and then you can apply ##\arcsin##.
 

What is the definition of "trigonometric ratios"?

Trigonometric ratios are mathematical relationships between the sides and angles of a right triangle. They are used to solve for unknown values, such as the length of a side or the measure of an angle.

What are the three main trigonometric ratios?

The three main trigonometric ratios are sine, cosine, and tangent. These ratios are defined as the ratio of two sides of a right triangle to a specific angle.

How do you use trigonometric ratios to solve for x?

To solve for x using trigonometric ratios, you need to identify which ratio to use based on the given information. Then, set up an equation with the known values and the trigonometric ratio. Finally, solve for x using algebraic manipulation.

What is the Pythagorean theorem and how is it related to trigonometric ratios?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is often used in conjunction with trigonometric ratios to solve for unknown values in a right triangle.

What are some real-life applications of using trigonometric ratios to solve for unknown values?

Trigonometric ratios are used in a variety of fields, such as engineering, physics, and navigation. They can be used to calculate the height of a building, the distance between two objects, or the angle of elevation or depression of an object. They are also used in construction and surveying to ensure accurate measurements and angles.

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