Quiz 7: IMO Mock Trigonometric Math Quiz

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Created by Isabelle Yeong on May 19th 2015

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Please answer the following questions based on the trigonometric equation below:

Question 1. Would you convert the cosecant function to the sine function to solve the trigonometric equation above?

Yes.

No.

Perhaps.

Clear selection

Question 2: Do you think the trigonometric identity 1+cot²x=csc²x would be useful in solving this problem?

Yes.

No.

Clear selection

Question 3: Which of the following method(s) is/are possible to use to solve the given trigonometric equation?

Differentiation +Trigonometric Identities

AM-GM Inequality+Trigonometric Identities

Strictly Trigonometric Identities

Question 4. If you chose the "strictly trigonometric identities method", would you expand sin 9x as sin 9x = 3sin 3x - 4(sin³ 3x)?

Yes.

No.

Clear selection

Question 5. If you chosen the "AM-GM Inequality + Trigonometric Identities method", which of the following terms do you think would require the AM-GM inequality to handle them?

sin 9x

5sin 3x

9tan²x

csc²x

Question 6. What are the solutions for this problem?

0, π/3(1+n), where n is an integer.

0, nπ, where n is an integer.

π/6(12-5n), π/3(1+n), where n is an integer.

π/6(12-5n), π/6(12-n), where n is an integer.

Clear selection

Question 7. Please rate the difficulty on this problem on a scale from 1 to 5 with 5 being the highest level of difficulty and 1 being the lowest level of difficulty.

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