Solve Trigonometry equations with (Trig) ax = b

Discussion of the trig form equation αx0 = b is interpreted as a form of a trogonometric equation such as sin αx0 = b, cos αx0 = b or tan αx0 = b. In this article a more complex form will also be developed.

Example 1.
Determine the set of completion equations sin x0 = ½, for 0 ≤ x ≤ 360.
Answers:
Sin x0 = ½
Sin x0 = sin 300
       x  = 30 + n . 360, or x = (180 -30) + n . 360
for 0 ≤ x ≤ 360. Then by choosing the appropriate n, x = 30 or x = 150 is obtained. So, the set of solutions is {30, 150}.

Example 2.
Determine the set of completion equations cos 2x0=-1/2 √3 , for 0 ≤ x ≤ 360.

Answers:


For 0 ≤ x ≤ 360, then by selecting the appropriate n, obtained
x = 75, 75 + 180 or x = -75 + 180, -75 + 2 . 180
x = 75 , 255 or x = 105, 285
so, the set of resolutions is {75, 105, 255, 285}

Example 3.
Determine the set of completion equations tan3x0=-√3, for 0 ≤ x ≤ 360.
Answers

for 0 ≤ x ≤ 360. Then by choosing the appropriate,
X = 40, 40 + 60, 40 + 2 . 60, 40 + 3 . 60, 40 + 4. 60, 40 + 5 . 60
    = 40, 100, 160, 220, 280, 340
so, the set of resolutions is {40, 100, 160, 220, 280, 340}.

Example 4.
Determine the set of completion equations sin (x – 15)0=1/2 √3 , for 0 ≤ x ≤ 360.
Answers:


for 0 ≤ x ≤ 360. Then by choosing the appropriate,
x= 75  or x = 135
so, the set of resolutions is {75, 135}.

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