How do you solve #2 cos x - 5 sin x = 3 #?

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Answer 1 · 2015-05-21T02:21:06

#f(x) = cos x - (5/2)sin x = 3/2#

Call a the arc whose tan is #tan a = 5/2 --> a = 68.20# deg

#(cos x.cos a - sin a.sin x)# = (3cos a)/2# =

= #(3(0.37))/2 = 0.56#

Finally,# cos (x + a) = cos (x + 68.20) = 0.56 = +-cos 55.94#

a.#( x + 68.20) = 55.94 -> x = - 12.26#

b.# (x + 68.20) = - 55.94 -> x = - 124.14.#