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Snowcat [4.5K]
3 years ago
9

The choir teacher is arranging the Junior and Senior choir members in equal rows for an upcoming concert. Each row will contain

all Juniors or all Seniors and not a mix of both. What is the greatest number of students that could be in each row so that all rows contain the same number of students? Explain or justify your reasoning.
Mathematics
1 answer:
ANTONII [103]3 years ago
7 0

The answer is 9

both 81 and 63 are dividable by 9, and nothing higher

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The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.

sec(<em>x</em>) = csc(<em>x</em>)

By definition of secant and cosecant,

1/cos(<em>x</em>) = 1/sin(<em>x</em>)

Multiply both sides by sin(<em>x</em>) :

sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)

As long as sin(<em>x</em>) ≠ 0, this reduces to

sin(<em>x</em>)/cos(<em>x</em>) = 1

By definition of tangent,

tan(<em>x</em>) = 1

Solve for <em>x</em> :

<em>x</em> = arctan(1) + <em>nπ</em>

<em>x</em> = <em>π</em>/4 + <em>nπ</em>

(where <em>n</em> is any integer)

In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of

<em>x</em> = <em>π</em>/4   <u>or</u>   <em>x</em> = 5<em>π</em>/4

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KengaRu [80]

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Step-by-step explanation:

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