There is something about a question not being graded that makes the students aggressive and risky. That can create the conditions for some of the best thinking. There are many days when I think grades and points and the division between problems that I will “collect and grade” versus the ones that I will not.

In the system in which I exist, sometimes bonus questions on formative assessments are the only way to really perplex a student – to push them at the risk of pushing each student beyond their current ability to reason, but still get a solid effort.

On today’s quiz, I added the following question as a bonus:

If you type “Tan 90″ into a calculator, you will get an error message. Knowing what you know about trig, discuss the possible reasons that taking the tangent of a right angle in a triangle would make your calculator show an error message.”

This isn’t something that has come up in any of our discussions. I would like to share with you some of my student’s answers.

From James: “It has an opposite which is the hypotenuse, but it has two adjacents so you wouldn’t know which one to use unless you put it in the calculator.”

From Tyler: “There is no such thing because when you plug in Cos 90 you get 0 and when you plug in Sin 90 you get 1. Maybe it is because since Tangent is TOA, it tries to add up to 90, so like opposite is 30 degrees and adjacent is 60 degrees.”

From Brianna: “Because Tan 90 would be opposite/adjacent, but the opposite side of the 90-degree angle is the hypotenuse and you can’t have the hypotenuse on top.”

From Jeremy: “It shows an error message because the right angle on a triangle doesn’t have a defined opposite or adjacent side length because the angle is touching both legs.”

From Lauren: “With tangent, you are finding opposite/adjacent. Those are the legs, and that 90-degree angle is being made by the legs.”

From Dayna: ” There could be an error because the opposite of the right angle is also the hypotenuse of the triangle.”

From Ally: It’s not clear where the negative idea comes from, but it is curious that in a Trig world of decimals and fractions, 90 in the other functions gives 1 and 0.

From Victor

Perhaps Josh’s picture says it all.

Now, the next question: If the “two-adjacent-sides-so-the-calculator-doesn’t-know-which-you-mean…” explanation wins out…

…then why don’t we get an error message for Cos 90?

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