How Can I Solve for F and X Using Trigonometric Identities?

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SUMMARY

The discussion focuses on solving for the force (F) and angle (X) using trigonometric identities derived from vector components. The equations FcosX = 4.1 and FsinX = 6.4 are established. To find F, the Pythagorean Theorem is applied, leading to the formula F = sqrt((6.4)^2 + (4.1)^2). This method confirms the relationship between the components of the force vector and the resultant force.

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  • Understanding of trigonometric functions (sine and cosine)
  • Familiarity with vector resolution and components
  • Knowledge of the Pythagorean Theorem
  • Basic algebra for manipulating equations
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  • Learn about trigonometric identities and their applications in physics
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Homework Statement



I have resolved three vectors to get the final equations with two unknowns.

F [force]
X [Angle]

FcosX = 4.1
FsinX = 6.4


Homework Equations





The Attempt at a Solution



Here is what I tried to do but failed miserably.

sinX=6.4/F
X=arcsin(6.4/F)

cosX=4.1/F
X=arccos(4.1/F)

I tried to solve for X = X --- but then I have no idea how to solve for F.
 
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fs93 said:

Homework Statement



I have resolved three vectors to get the final equations with two unknowns.

F [force]
X [Angle]

FcosX = 4.1
FsinX = 6.4


Homework Equations





The Attempt at a Solution



Here is what I tried to do but failed miserably.

sinX=6.4/F
X=arcsin(6.4/F)

cosX=4.1/F
X=arccos(4.1/F)

I tried to solve for X = X --- but then I have no idea how to solve for F.



Ok well, you solved for X in terms of F. To solve for F use the Pythagorean Theorem. (6.4) is one component of the force vector and (4.1) is the other component. Therefore, F=sqr((6.4)^2+(4.1)^2). We know that this is a valid step because we add vectors tip to tail (in this case creating a right angle).
 

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