Math Is Fun Forum

bingbong

Member

Registered: 2016-03-04

Posts: 8

Geometry- Trigonometry

I need an explanation for this question. I have no idea how to start.

Explain why we must have \ot^2 x + 1 = csc^2x for any x such that x is not an integer multiple of 180 degrees.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Geometry- Trigonometry

hi bingbong

Start with a right angled triangle and 'O', 'A' and 'H' having their usual meanings.

Write out the usual Pythagoras formula and divide by O squared.

That proves the formula for angles 0 up to 90.

Outside that range the trig values are defined by symmetry so eg. sin^2(120) = sin^2(60).  Therefore the result continues to hold for all angles.

Bob

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