Why Was Six Afraid of Seven

Why was 6 afraid of 7? sin(21) sin(21°) = sin(21°) = a/c cos(69°) = a/c sin(21) = cos(69) sin(21) = cos(69) = cos(429) +360 sin(21) = cos(429) = cos(789) +360 cos(789)

A man explains the classic “Why was 6 afraid of 7?” joke using a unit-circle trigonometry diagram. He derives sin(21) = cos(69), then adds 360 degrees twice to reach cos(789), making the punchline sound like “cos 789” — “because seven ate nine.” EN: A man explains the classic “Why was 6 afraid of 7?” joke using a unit-circle trigonometry diagram. He derives sin(21) = cos(69), then adds 360 degrees twice to reach cos(789), making the punchline sound like “cos 789” — “because seven ate nine.”

Why was six afraid of seven? Sign 21. Ha ha ha. Do you guys get it? Let me explain. So if we have a unit circle and we draw a triangle on it, let's make this angle right here equal to 21 degrees. That make this angle down here 69 degrees nice. But that's not the punchline. Next, let's give these sides a, b, and c. The sign of 21 degrees is gonna be the opposite a over the hypotenuse c. And the cosine of the 69 degrees is gonna be the adjacent a over the hypotenuse c. So they're both a over c. So we know the sign 21 is equal to cosine 69. So let's get rid of this work and scoot these over. Now 69 degrees is this angle right here. If we were to rotate all the way around once and then go back to here, that would end up being the 69 plus 360, which gives us the cosine of 429. Let's scoot this over. So now let's go around two times. I'm gonna go around once to get the 429 and then again, I'll add another 360. That's equal to 789. So let's get rid of this and squish these together. So sine of 21 is the same thing as cos 789. So once again, why was 6 afraid of 7? Coast 789, how exciting.

• @pokupkabitka / 18532 2022-11-27