# Solutions to sin/cos/tan

1. Oct 15, 2014

### physior

hello

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!

2. Oct 15, 2014

### phinds

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

3. Oct 15, 2014

### Staff: Mentor

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.

4. Oct 16, 2014

### physior

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

5. Oct 16, 2014

### Staff: Mentor

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

6. Oct 16, 2014

### physior

by the solutions of sinθ, I mean θ!

7. Oct 16, 2014

### phinds

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

8. Oct 16, 2014

### Staff: Mentor

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.