Solutions for Sin/Cos/Tan: Understanding and Applying the OR Rule

[physior]

hello

I read in textbook that
the solutions of sinθ is k360+θ or k360+180-θ
the solutions of cosθ is k360+θ or k360-θ
the solutions of tanθ is k180+θ

1) what does the OR mean exactly? to get all the solutions we ADD (so AND, not OR) the expressions of the solutions? I understand OR, as if I can use only one of those (eg. for sinθ I can use only k360+θ OR k360+180-θ) and I will find all the solutions?
2) does these apply when θ is negative? so if the solution I get from the calculator is negative, do I process it with its negative sign?

thanks!

 

[phinds]

I assume it just means that sinθ = sin(360+θ) = sin(360+180-θ), etc

 

[Mark44]

hello

I read in textbook that
the solutions of sinθ is k360+θ or k360+180-θ
the solutions of cosθ is k360+θ or k360-θ
the solutions of tanθ is k180+θ

1) what does the OR mean exactly? to get all the solutions we ADD (so AND, not OR) the expressions of the solutions?

No, "or" is correct. For example, if x² = 4, then x = 2 OR x = -2. x can be either one of those values. "And" is not applicable because x can't simultaneously be equal to 2 and -2.

I understand OR, as if I can use only one of those (eg. for sinθ I can use only k360+θ OR k360+180-θ) and I will find all the solutions?
2) does these apply when θ is negative? so if the solution I get from the calculator is negative, do I process it with its negative sign?

Yes. This possibility is covered when k is negative. It will usually be specified that k is an integer, which includes the negative integers.

 

[physior]

No, "or" is correct. For example, if x² = 4, then x = 2 OR x = -2. x can be either one of those values. "And" is not applicable because x can't simultaneously be equal to 2 and -2.
Yes. This possibility is covered when k is negative. It will usually be specified that k is an integer, which includes the negative integers.

I am talking about the theta to be negative! not the k (which I know it must belong to Z)

 

[Mark44]

I am talking about the theta to be negative! not the k (which I know it must belong to Z)

Then you need to be clearer in what you're asking.

I read in textbook that
the solutions of sinθ is k360+θ or k360+180-θ
the solutions of cosθ is k360+θ or k360-θ
the solutions of tanθ is k180+θ

"The solutions of sinθ" doesn't make any sense. When we talk about solutions, we're talking about values that make an equation a true statement. There are no equations in what you wrote.

 

[physior]

by the solutions of sinθ, I mean θ!

 

[phinds]

by the solutions of sinθ, I mean θ!

But θ is NOT a "solution to sinθ". If θ is 45 degrees, for example, sin θ is .707

 

[Mark44]

by the solutions of sinθ, I mean θ!

As I already said, sinθ is not an equation, so it doesn't make sense to talk about solutions of an expression. In the expression sinθ, θ is the argument or parameter of the sine function.