How would I solve for Length? simple math equation involving sin/cosine?

In summary, the conversation discusses how to solve for L in the expression sintheta=L/sq.rt(x^2+L^2). The person also asks about using the equation costheta=L/sq.rt(x^2+L^2) and whether it would provide the same answer. The conversation mentions that the equations involve the same triangle and the given information of a 90 degree angle between the y and x axis, but an unknown angle. The suggested solution is to square both sides of the equation, rearrange, and factor out L to obtain an answer in terms of x and \theta.
  • #1
jcfor3ver
30
0

Homework Statement

How would I solve for L in this expression:

sintheta=L/sq.rt(x^2+L^2) ?



Homework Equations


sintheta=L/sq.rt(x^2+L^2) ?




The Attempt at a Solution


and if they have the same angle between them would solving for L create an equal answer using:
costheta=L/sq.rt(x^2+L^2)
??

given there is a 90 degree angle between the y and x axis, but the angle is unknown, but these two equations involve the same triangle.

Solving I received sq.rt((-x^2+(costheta/x))^2)=L but i think its wrong
 
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  • #2
Try squaring both sides, rearranging a bit and then factoring out L. You'll have an answer in terms of x and [itex]\theta[/itex]
 

1. How do I determine the length of a triangle using sine and cosine?

To solve for the length of a triangle using sine and cosine, you will need to know the measure of one angle and at least one side length. Then, you can use the sine or cosine function with the given angle and side length to find the missing side length. Remember to use the inverse function (arcsine or arccosine) to find the angle measure if the side length is given.

2. Can I use sine and cosine to find the length of any shape?

No, sine and cosine can only be used to find the length of a triangle. These functions are specifically designed for right triangles and cannot be applied to other shapes.

3. What is the difference between using sin versus cos to solve for length?

The main difference between using sin and cos to solve for length is the angle that is used. Sine uses the opposite side length and the hypotenuse, while cosine uses the adjacent side length and the hypotenuse. Depending on the given information, one function may be more useful than the other.

4. How do I know if I need to use sine or cosine to solve for length?

You can determine which function to use by looking at the given information. If you have the angle and the opposite side length, use sine. If you have the angle and the adjacent side length, use cosine. If you have both the opposite and adjacent side lengths, you can use either function.

5. Can I use sine and cosine to find the length of a non-right triangle?

No, sine and cosine can only be used to find the length of a right triangle. If you have a non-right triangle, you will need to use other trigonometric functions such as tangent, cotangent, secant, or cosecant to find the missing side length.

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