Solving an equation involving sin and cos terms

In summary, the person is asking if there is a non-numerical way to solve the equation 144 - 90sin x - 155.8cos x = 0. They suggest writing it in a different form and squaring both sides to find the value of cos x, then taking the arccosine to find x. They also mention the possibility of obtaining roots that do not satisfy the original equation when squaring both sides.
  • #1
nokia8650
219
0
Hi

I was wondering if there is a non-numericla way to solve the following equation:

144 - 90sin x - 155.8cos x = 0

Thanks
 
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  • #2
nokia8650 said:
Hi

I was wondering if there is a non-numericla way to solve the following equation:

144 - 90sin x - 155.8cos x = 0

Thanks
That's not a nice equation but here's what I might do: write it as 90 sin x= 144- 155.8 cos x
[itex]90\sqrt{1- cos^2 x}= 144- 155.8 cos x[/itex] and square both sides to get [itex]8100(1- cos^2 x)= 20736- 44870.4cos x+ 24273.64cos^2 x[/itex]. Solve that quadratic equation for cos x and then take the arccosine to find x. When you square both sides of an equation, that new equation may have roots that do not satisfy the original equation.
 
  • #3
Thank you!
 

1. How do you solve an equation involving sin and cos terms?

To solve an equation involving sin and cos terms, you must use trigonometric identities and algebraic techniques to manipulate the equation until it is in a form where you can isolate the variable. This may involve using the Pythagorean identity, double angle formulas, or other trigonometric identities.

2. What are the key steps in solving an equation involving sin and cos terms?

The key steps in solving an equation involving sin and cos terms are:
1. Simplify the equation by using trigonometric identities.
2. Use algebraic techniques to isolate the variable.
3. Check your solution by plugging it back into the original equation.

3. Can you use a calculator to solve an equation involving sin and cos terms?

Yes, you can use a calculator to solve an equation involving sin and cos terms. However, it is important to have a basic understanding of trigonometric identities and how to manipulate equations before relying on a calculator.

4. Are there any special cases when solving an equation involving sin and cos terms?

Yes, there are a few special cases when solving an equation involving sin and cos terms. These include when the equation has an identity solution (such as sin x = sin x) or when the equation has an extraneous solution (such as sin x = -1). It is important to check for these cases and eliminate any extraneous solutions.

5. Can you use the inverse sine or cosine function to solve an equation involving sin and cos terms?

Yes, you can use the inverse sine or cosine function to solve an equation involving sin and cos terms. However, this method may not always yield the complete solution set, so it is important to check for any additional solutions by using trigonometric identities and algebraic techniques.

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