How do you find all solutions of the following equation in the interval [0,2pi] of $sin x + cos x = 0$ ?

Question

2461 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-15T07:41:59

$x=135^@, 315^@$ OR
$x=(3pi)/4, (7pi)/4$

Find the solution within $0^@$ up to $360^@$

$sin x+cos x=0$
$sin x=-cos x$

divide both sides by $cos x$
$sin x/cos x=-cos x/cos x$

$tan x=-1$

$x=tan^-1 (-1)$

$x=135^@$ because $tan 135^@=-1$
also
$x=315^@$ because $tan 315^@=-1$

Take note: $135^@=(3pi)/4$ and $315^@=(7pi)/4$

God bless America .....

How do you find all solutions of the following equation in the interval [0,2pi] of sin x + cos x = 0 sin x + cos x = 0?