What is the next fraction in each following patterens 1/40, 4/40, 9/40, 16/40, 25/40

1 answer:

3 0

The numerator (top number of the fraction) is adding up by odd numbers in order.
From 1/40 to 4/40 you add 3, from 4/40 to 9/40 you add 5, from 9/40 to 16/40 you add 7, and from 16/40 to 25/40 you add 9.
The next number to add would logically be 11. So from 25/40 you would go to 36/40.
36/40 is your next fraction.

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Answer:

Step-by-step explanation:

If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...

Anyways, the half angle identity for tangent is

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There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.

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$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{1+(-\frac{4}{5}) }$ which simplifies a bit to

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{5}{5} -\frac{4}{5} }$ and a bit more to

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{1}{5} }$

Bring up the lower fraction and flip it to divide to get

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