# Solve Trigonometry equations with (Trig) ax = b

Discussion of the trig form equation αx

^{0}= b is interpreted as a form of a trogonometric equation such as sin αx^{0}= b, cos αx^{0}= b or tan αx^{0}= b. In this article a more complex form will also be developed.**Example 1.**

Determine the set of completion equations
sin x

^{0}= ½, for 0 ≤ x ≤ 360.
Answers:

Sin x

^{0}= ½
Sin x

^{0}= 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 2x

^{0}=-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
tan3x

^{0}=-√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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