Which of the following are true statements? Select all that apply.

A) The cosecant graph has a local minimum when the sine graph has a local minimum.

B) The cosecant graph has a local minimum when the sine graph has a local maximum.

C) The cosecant graph has a local maximum when the sine graph has a local maximum.

D) The cosecant graph has a local maximum when the sine graph has a local minimum.

Which is the same for both the sine and cosecant function?

Question

23-07-2018
Mathematics

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Which of the following are true statements? Select all that apply.

A) The cosecant graph has a local minimum when the sine graph has a local minimum.

B) The cosecant graph has a local minimum when the sine graph has a local maximum.

C) The cosecant graph has a local maximum when the sine graph has a local maximum.

D) The cosecant graph has a local maximum when the sine graph has a local minimum.

Which is the same for both the sine and cosecant function?

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DeanR DeanR · Answer 1 · 2018-07-23T02:51:27+02:00

DeanR DeanR

23-07-2018

Since sine and cosecant are reciprocals, when one has a maximum the other has a minimum and vice versa.

That's choices B & D

Not sure what the question at the end is asking; at 90 degrees and also at -90 degrees the values of sine and cosecant are equal.

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codiepienagoya codiepienagoya · Answer 2 · 2021-10-28T15:24:06+02:00

This cosecant descends towards the height of the sine curve and ascends to the lowest of a sine curve. Following sketching a cosecant curve with the asymptotes and reciprocal as guides, we may delete those superfluous lines, leaving only [tex]\bold{y = \cos x}[/tex].

Its cosecant of the angles in a right-angled triangle is indeed the length of the hypotenuse based on the length of said backside its angle.
This cosecant graph does have a local minimum, while the sine graph does have a local maximum.
The cosecant graphs do have a local maximum, while the sine graph does have a local minimum.

Therefore, the final answer is "Choice B and Choice D".

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