Diketahui
sehingga diperoleh
![table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses x plus 30 degree close parentheses plus cos open parentheses x plus 30 degree close parentheses end cell equals 0 row cell sin open parentheses x plus 30 degree close parentheses end cell equals cell negative cos open parentheses x plus 30 degree close parentheses end cell end table](data:image/png;base64,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)
Berdasarkan aturan sudut berelasi yaitu
maka
diperolah sebagai berikut.
sin(x+30∘)sin(x+30∘)sin(x+30∘)sin(x+30∘)====−cos(x+30∘)sin(270∘−(x+30∘))sin(270∘−x−30∘)sin(240∘−x)
Penyelesaian persamaan sinus
x+30∘x+x2xxx=====240∘−x+k⋅360∘ 240∘−30∘+k⋅360∘210∘+k⋅360∘2210∘+k⋅2360∘105∘+k⋅180∘
atau
x+30∘x+30∘x+30∘x−x0=====(180∘−(240∘−x))+k⋅360∘ 180∘−240∘+x+k⋅360∘−60∘+x+k⋅360∘−60∘−30∘+k⋅360∘−90∘+k⋅360∘
(tidak bisa digunakan untuk mencari nilai x)
dengan k merupakan bilangan bulat.
Kemudian uji berbagai nilai k dan pilih nilai x yang terletak pada interval
.
k=0 →k=1 →k=2 →k=−1 →x=105∘+k⋅180∘x=105∘+0⋅180∘x=105∘+0∘x=105∘x=105∘+1⋅180∘x=105∘+180∘x=285∘x=105∘+2⋅180∘x=105∘+360∘x=465∘x=105∘+(−1)⋅180∘x=105∘−180∘x=−75∘(memenuhi)(memenuhi)(tidak memenuhi)(tidak memenuhi)
Jadi nilai
yang memenuhi persamaan
pada interval
adalah
.