# 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:


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

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And then, both side divide with $r²$, it will become:

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

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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 ==$a \over r$== or ==$b \over r$== is ==$sin\ x$==, and another one is ==$cos\ x$==.

And don't forget the square, so it will shows ==$sin^2\ x$ and $cos^2\ x$==.

And this is Trigonometric Identities:

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$$sin^2\ x + cos^2\ x = 1$$

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## 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.