- #1

CatWhisperer

- 40

- 1

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

## Homework Statement

Determine if the following relation is a function of [itex]x[/itex] on [itex]\mathbb R[/itex]:

[tex]sin(x + y)=1[/tex]

## The Attempt at a Solution

Rearrange to make [itex]y[/itex] the subject:

[tex]y = sin^{-1}(1) - x[/tex]

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 [itex]m = 1[/itex]; however, the solution that has been given states that this is not a function, because for all [itex]x\in\mathbb R[/itex] there exist inﬁnitely many [itex]y[/itex] values.

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

Thanks in advance.