How do you use inverse trig functions to solve equations?

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Jim H Share
Nov 16, 2017

#sinx=n# if and only if #x=arcsinn + 2 pi k# for some integer #k#

or #x=(pi-arcsinn) + 2 pi k# for some integer #k#

#cosx=n# if and only if #x=arccosn + 2 pi k# for some integer #k#

or #x=(pi+arccosn) + 2 pi k# for some integer #k#

#tanx=n# if and only if #x=arctan n + pi k# for some integer #k#

and so on.

So,: Solve #7sinx-5 = 0#

#7sinx-5 = 0#
#7sinx = 5#
#sinx = 5/7#

#x=arcsin(5/7) +2 pi k# for integer #k#
or #(pi-arcsin(5/7)) +2 pi k# for integer #k#

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