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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