"Ok class. You may start."; Stanford Intellectual Vitality

"Ok class. You may start."

I quickly turned the paper over and there was only 1 problem:

"Show that (Tan(x+y)=x) = -(x^2)/(x^(2)-1)"

As it was a test over derivatives, I knew I'd have to apply some sort of derivative rule to solve this beast. As I couldn't isolate y, I decided that implicit differentiation would be the best approach. But when I reached what seemed like a dead end in the form of -sin(x+y), I almost gave up. I couldn't simplify any further. 5 min left. I started to worry. Then it hit me.

"What if I draw a triangle?"

Since tangent is opposite over adjacent, the opposite side must equal x and the adjacent is 1. The hypotenuse would then be √(x^2 + 1). Sin(x+y) would then equal x/√(x^2 + 1). Squaring the top and bottom would result in x^(2)/(x^2 + 1). Then add a negative sign because I had negative sin, and there lay my answer. I quickly wrote down the answer and submitted my paper.

The A was a nice gift, but my true reward was the application of other disciplines of mathematics to help reach what seemed like an improbable solution. Never would I have thought that a quick lesson in Pre-Calculus would save my butt and propel me to the top of my class. Our teacher said to think outside the box; how about outside the triangle?

Feedback and thought are very helpful, as English really isn't my strongest subject! Please don't be afraid to be critical as well!

Hello,

So, when I was in high school, I was always taught to use triangles to help solve pre-calc and calc problems. Because of this, I am not sure how this is an intellectual vitality question as thinking like this is necessary to solve complex mathematical questions. When tackling this question, I always encourage my clients to use a non-classroom example. Why? Admissions officers already have enough information on your academic prowess. They can see your grades, mid-year reports, test scores, teacher rec's, the last thing they really want to see is another academic attribute. To tackle this question better, think about an experience that you have had where you had an "Ah-hah" moment. A moment that changed your thinking and one that really sparked a great interest in you. -Admissions Advice Online

Hope this helps