sinx+cosx=0 for 0<x<360 Watch

NewCrack
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#1
Report Thread starter 7 years ago
#1
how do i do this? i keep getting it wrong? what error have i made in my working?

sinx + cosx = 0 i applied the tanx = sinx/cosx identity so i divided by cosx

tanx + 1 =0
tanx = -1
x = arctan(-1) =-45

then i got theta = 45 and 225:confused:

but the book says it is 135 and 315.
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vc94
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#2
Report 7 years ago
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The period of the tan graph is 180.
So you get other solutions by adding or subtracting multiples of 180 to your principal value of -45.
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nuodai
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You found that x=-45^{\circ} so why did you deduce that x=45^{\circ} is a solution?

Note that \tan x = \tan (x + 180^{\circ}), so you need to add 180 a few times to get all the solutions in the given range.
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NewCrack
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#4
Report Thread starter 7 years ago
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(Original post by nuodai)
You found that x=-45^{\circ} so why did you deduce that x=45^{\circ} is a solution?

Note that \tan x = \tan (x + 180^{\circ}), so you need to add 180 a few times to get all the solutions in the given range.
i don't know >.> i was thinking about symmetry
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nuodai
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(Original post by NewCrack)
i don't know >.> i was thinking about symmetry
I see. That only works for \cos x, since \cos (-x) = \cos x; but for f(x)=\sin x or \tan x we have f(-x)=-f(x) so it doesn't work.
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kamaldeepwidabeep
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#6
Report 7 years ago
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nah dude tan has rotational symetry. so you have to add and subtract 180 to ur orriginal answer untill you get all the answerr within the given range
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