# Is sin(x + y) = 1 a function of x on R?

1. Mar 22, 2014

### CatWhisperer

Is "sin(x + y) = 1" a function of x on R?

1. The problem statement, all variables and given/known data

Determine if the following relation is a function of $x$ on $\mathbb R$:

$$sin(x + y)=1$$

3. The attempt at a solution

Rearrange to make $y$ the subject:

$$y = sin^{-1}(1) - x$$

Then, I simply calculated some points and plotted a graph, which was linear. The points I used:

(-3, 4.57)
(-2, 3.57)
(-1, 2.57)
(0, 1.57)
(1, 0.57)
(2, -0.43)
(3, -1.43)
(4, -2.43)

As you can see, this would produce a linear graph with a gradient of $m = 1$; however, the solution that has been given states that this is not a function, because for all $x\in\mathbb R$ there exist inﬁnitely many $y$ values.

Appreciate any help in explaining why this is so, as I am stumped :)

2. Mar 22, 2014

### SammyS

Staff Emeritus
For how many values of θ is sin(θ) = 1 ?

3. Mar 22, 2014

### LCKurtz

Or, to elaborate on SammyS's question, if $x=0$ can you find more than one $y$ that works?