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

Question

2310 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 .....