Solving Simultaneous equations with cos() and sin()

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  • Thread starter Micheal_Leo
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  • #1
Micheal_Leo
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Hello

I have two equations given below and answer is also given solve by simultaneously

i am not sure how this happen


please guide thank you


微信图片_20231030135934.jpg
 
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  • #2
Use the identity
[tex]\sin^2\theta_s+\cos^2\theta_s=1[/tex]
 
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  • #3
anuttarasammyak said:
Use the identity
[tex]\sin^2\theta_s+\cos^2\theta_s=1[/tex]
thank you for reply , first have to take square on both sides of equation 1 and 2 than use identity ?
 
  • #4
Get
[tex]V sin\theta_s, V cos\theta_s[/tex]
exlpcit and use the identity.
 
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  • #5
anuttarasammyak said:
Get
[tex]V sin\theta_s, V cos\theta_s[/tex]
exlpcit and use the identity.
thank you very much perfectly got it
 
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1. How do you solve simultaneous equations involving cos() and sin() functions?

To solve simultaneous equations involving cos() and sin() functions, you can use the trigonometric identities and properties of these functions. By manipulating the equations and applying these identities, you can often simplify the equations to a point where you can solve for the variables.

2. Can you provide an example of solving simultaneous equations with cos() and sin()?

Sure! For example, if you have the equations:
cos(x) + sin(y) = 1
2cos(x) - sin(y) = 0
You can manipulate these equations using trigonometric identities to solve for the values of x and y.

3. Are there any specific strategies to keep in mind when solving these types of equations?

One important strategy is to try to eliminate one of the trigonometric functions by combining the equations in a way that cancels out one of the functions. This can simplify the equations and make it easier to solve for the variables.

4. What should I do if I encounter a system of equations with multiple trigonometric functions?

If you encounter a system of equations with multiple trigonometric functions, you can try to isolate one of the functions in one of the equations and substitute it into the other equation. This can help you reduce the number of variables and make it easier to solve the equations.

5. Are there any online tools or resources that can help me solve simultaneous equations with cos() and sin()?

Yes, there are various online calculators and software programs that can help you solve simultaneous equations involving cos() and sin() functions. These tools can provide step-by-step solutions and help you check your work.

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