chefo's Homework

chefo's question photo

Just put it here so I don't have to keep switching windows.

Preface

So, this question is actually testing you whether you remembered Trigonometric Identities, which is a key formula to solve this question.

I'm not sure what kind of Maths lesson you had learnt, but I will prove it from the ground up, so that you may learn how it comes.

Proving Trigonometric Identities

So, I believe you know that famous Pythagorean theorem. As following shows:

$$a^2+b^2=r^2$$

And then, both side divide with

$r²$, it will become:

$$\frac{a^2}{r^2}+\frac{b^2}{r^2}=1$$

At here, we don't need to worry about which border (

$a$ and/or

$b$) is longer/shorter, because we got both.

Since the

$r$ is hypotenuse, and it got divided by both

$a$ and

$b$.

That means, one of

$\frac{a}{r}$ or

$\frac{b}{r}$ is

$sinx$, and another one is

$cosx$.

And don't forget the square, so it will shows

$si{n}^{2}x$ and

$co{s}^{2}x$.

And this is Trigonometric Identities:

$$si{n}^{2}x+co{s}^{2}x=1$$

Back to chefo's question

Let's look at the context, now we can know that

$y=1$, because we just proved that what number we just got.

And this means, mo matter how big or how small the

$x$ is, the

$y$ will always be

$1$, thus this is a stright line parallel to the x-axis and passing through 1 unit of the y-axis, which is the graph H.