What is the general solution for 0=asin(x)+bcos(x) ?

The general solution for 0=asin(x)+bcos(x) is x=arctan(-b/a)+pin

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0=asin(x)+bcos(x)

0 = a sin (x) + b cos (x)

x = arctan (- \frac{b}{a}) + πn

Solution steps

0 = a sin (x) + b cos (x)

Switch sides

a sin (x) + b cos (x) = 0

Rewrite using trig identities

a tan (x) + b = 0

Move

b

to the right side

a tan (x) = - b

Divide both sides by

a; a \neq = 0

tan (x) = - \frac{b}{a}; a \neq = 0

Apply trig inverse properties

x = arctan (- \frac{b}{a}) + πn

2 sin^{2} (x) + 9 cos (x) - 6 = 0

tan (θ) = \frac{- 4}{- 3}

cos^{2} (x) + 3 cos (x) + 2 = 0

5 tan^{2} (x) + 5 = 10

sin (6 x) + sin (4 x) + sin (2 x) = 0

What is the general solution for 0=asin(x)+bcos(x) ?
The general solution for 0=asin(x)+bcos(x) is x=arctan(-b/a)+pin