Rewrite the trigonometric expression as an algebraic equation

In summary: You are tired and sick, and so you need to be extra careful to write clearly.In summary, the conversation discusses how to write trigonometric expressions as equations in terms of x and y, and whether it is a good practice to do so. It also clarifies the importance of using clear and conventional notation in mathematical work.
  • #1
Tyrion101
166
2
What is this asking for? Is it asking for the trig expression in the form of x and y? Or is it asking for something else?
 
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  • #2
Tyrion101 said:
What is this asking for? Is it asking for the trig expression in the form of x and y? Or is it asking for something else?
I don't see how it is possible to write an expression (trig or otherwise) as an equation. They are different kinds of things.

It would help if you told us what the problem is. If it is a homework problem, it needs to be posted in the Homework & Coursework sections (Precalc).
 
  • #3
When I'm solving trig equations I will simply rewrite them in terms of x and y, so that they are easier to read, then plug back in the trig values when I'm done factoring and otherwise simplifying the problems. Is this a bad habit? I'm just confused as to if this is what it is talking about or if it is something else. Cos(arcos + arcsin) edit I used the wrong term. I meant expression for both, I'm tired and a bit ill.
 
  • #4
Tyrion101 said:
When I'm solving trig equations I will simply rewrite them in terms of x and y, so that they are easier to read, then plug back in the trig values when I'm done factoring and otherwise simplifying the problems. Is this a bad habit?
No, this is good to do, as long as you are clear about what you are doing when you make the substitution, and then when you undo it. By that, I mean that you write something like "Let B = <whatever>..."
Tyrion101 said:
I'm just confused as to if this is what it is talking about or if it is something else. Cos(arcos + arcsin) edit I used the wrong term. I meant expression for both, I'm tired and a bit ill.
"Cos(arcos + arcsin)" is meaningless, though. arccos of what? arcsin of what? Each of these functions needs an argument; e.g., arccos(y) or arcsin(##\pi/2##).
 
  • #5
Tyrion101 said:
When I'm solving trig equations I will simply rewrite them in terms of x and y, so that they are easier to read, then plug back in the trig values when I'm done factoring and otherwise simplifying the problems. Is this a bad habit? I'm just confused as to if this is what it is talking about or if it is something else. Cos(arcos + arcsin) edit I used the wrong term. I meant expression for both, I'm tired and a bit ill.
You must be clear about what you say both to yourself and to other people. This means you need to use conventional notation. You must have a justifiable reason for assigning sines and cosines to x or y, and not simply do this for convenience of writing steps.
 
  • #6
Mark44 said:
No, this is good to do, as long as you are clear about what you are doing when you make the substitution, and then when you undo it. By that, I mean that you write something like "Let B = <whatever>..."

"Cos(arcos + arcsin)" is meaningless, though. arccos of what? arcsin of what? Each of these functions needs an argument; e.g., arccos(y) or arcsin(##\pi/2##).

Sorry, both arcos and sin have x's, I'm rather tired and sick at the moment. So anything left out just assume it wasn't on purpose.
 
  • #7
Tyrion101 said:
Sorry, both arcos and sin have x's, I'm rather tired and sick at the moment. So anything left out just assume it wasn't on purpose.
Like I said, your writing needs to be clear both to yourself and to others who read your work. You wrote something which was incomplete, and the readers will often not know what exact interpretation to make.
 

FAQ: Rewrite the trigonometric expression as an algebraic equation

What is a trigonometric expression?

A trigonometric expression is an equation that contains trigonometric functions, such as sine, cosine, and tangent, as variables. These expressions are used to represent relationships between angles and sides in a right triangle.

Why would I need to rewrite a trigonometric expression as an algebraic equation?

Rewriting a trigonometric expression as an algebraic equation allows you to solve for unknown variables and manipulate the equation using algebraic principles. This can be useful in solving complex trigonometric problems or simplifying equations.

How do I rewrite a trigonometric expression as an algebraic equation?

To rewrite a trigonometric expression as an algebraic equation, you will need to use trigonometric identities and the relationships between angles and sides in a right triangle. These identities can be found in a trigonometric table or derived using basic trigonometric principles.

Can all trigonometric expressions be rewritten as algebraic equations?

Yes, all trigonometric expressions can be rewritten as algebraic equations using trigonometric identities and principles. However, some expressions may be more complex and require more steps to rewrite than others.

Are there any tips for rewriting trigonometric expressions as algebraic equations?

Yes, it is helpful to familiarize yourself with common trigonometric identities and practice using them in various problems. It is also important to understand the relationships between angles and sides in a right triangle and how they can be represented using trigonometric functions.

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