Can We Cut Off The Ones?
tan 1 ∘ , tan 1 1 ∘ , tan 1 1 1 ∘ , tan 1 1 1 1 ∘
Which of the numbers above is the greatest?
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2 solutions
tan ( 1 1 1 1 ∘ ) = tan ( 3 1 ∘ ) the sign of tan ( 3 1 ∘ ) is positive as tan ( x ) is positive in the first quadrant. The sign of tan ( 1 1 1 ∘ ) is negative as tan ( x ) is negative in the second quadrant.
Also, tan ( x ) increases in the first quadrant so the maximum value is tan ( 1 1 1 1 ∘ )
Shouldn't the question read, "Which of these is the GREATEST" not "LARGEST"? Or do I have my terminology backwards?
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To you, what is the difference between these 2 terms?
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Well, if you owed $8,000,000 that is a lot of money. Your net worth would be $-8,000,000. It is a LARGE number that is LESS THAN 0. Having $8,000,000 in cash is a LARGE number that is GREATER THAN 0.
Tan(111), being negative, is Less Than tan(1,111), but it's [absolute] value is Greater Than tan(1,111).
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@Hazard Sharp – I am unaware of such a distinction. Do you have a reference for this English usage?
For clarity, I have edited the term to greatest.
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@Calvin Lin – No literary reference, just the memory of my calculus teacher pointing out that large numbers can be negative or positive. While 'greatest' implies value.
Thank you for your consideration.
There is no difference between greatest and largest.. The answer should be tan 11°
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Note that tan 1 1 ∘ < tan 3 1 ∘ = tan 1 1 1 1 ∘ .
Not a solution, but a suggestion. You could have made this question trickier by putting the last option as tan(1081). That way, people don't just look at the highest value for tangent and choose that because as you know, tan(1081)=tan(1). Otherwise, its a good question; it forced me to review my trigonometric complementary angle formulas (despite the fact that they are not used for this problem).