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. $(x + 68.20) = - 55.94 -> x = - 124.14.$

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