How do you find the intersections points of #y=-cosx# and #y=sinx#?

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Answer 1 · 2016-11-11T23:01:37

Please see the explanation.

Because #y = y# at the point of intersection, we can write the following equation:

#-cos(x) = sin(x)#

Divide both sides by #cos(x)#:

#-1 = sin(x)/cos(x)#

Use the identity #tan(x) = sin(x)/cos(x)#:

#tan(x) = -1#

This occurs at:

#x = (3pi)/4 + npi#

where n is any integer:

# n = ...,-3,-2,-1,0,1,2,3,...#

The y value is #sqrt(2)/2#, if n is even and #-sqrt(2)/2#, if n is odd.

Here is a graph that shows a few intersection points:
purple is y = -cos(x), orange is y = sin(x)