Solve Trigonometry equations with cos x^0 + b sin x^0 = c

To solve the equation in the form of a cos x0 + b sin x0 = c first, what must be done is to change the form of the equation a a cos x0 + b sin x0 = c to be,

k cos (x - α)0 = c


considering – 1 cos (x - α) 1, so that the equation can be solved must be fulfilled.


Example 1.
Determine the set of completion equations cos x0 – sin x0 = -1, for 0 x < 360.
cos x0 – sin x0 = -1
√2 cos (x – 315)0 = -1
cos (x – 315)0 = -1/2 √2
x – 315 = 135 + n . 360 or x – 315 = - 135 + n . 360
x = 450 + n . 360 or x = 180 + n . 360
The set of solutions is {90, 180}.

Example 2.
Determine the set of completion equations – cos x0 + 2 sin x0 = 2, for 0 x 360.
Answer:
– cos x0 + 2 sin x0 = 2
√5 cos (x – 116.6)0 = 2
cos (x – 116.6)0 = 2 / √5
cos (x – 116.6)0 = 0.894
x – 116.6 = 26.6 + n . 360 or x – 116.6 = -26.6 + n . 360
x = 143.2 + n . 360 or x = 90 + n . 360
The set of solutions is {90, 143.2}.

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