해법
3sin(5x)=−1,x<2π,0
해법
x=−50.33983…,x=5π+0.33983…,x=5−0.33983…+2π,x=53π+0.33983…,x=5−0.33983…+4π,x=55π+0.33983…,x=5−0.33983…+6π,x=57π+0.33983…,x=5−0.33983…+8π,x=59π+0.33983…,x=5−0.33983…−2π,x=5−π+0.33983…,x=5−0.33983…−4π,x=5−3π+0.33983…,x=5−0.33983…−6π,x=5−5π+0.33983…,x=5−0.33983…−8π,x=5−7π+0.33983…
+1
도
x=−3.89424…∘,x=39.89424…∘,x=68.10575…∘,x=111.89424…∘,x=140.10575…∘,x=183.89424…∘,x=212.10575…∘,x=255.89424…∘,x=284.10575…∘,x=327.89424…∘,x=−75.89424…∘,x=−32.10575…∘,x=−147.89424…∘,x=−104.10575…∘,x=−219.89424…∘,x=−176.10575…∘,x=−291.89424…∘,x=−248.10575…∘솔루션 단계
3sin(5x)=−1,x<2π,0
양쪽을 다음으로 나눕니다 3
3sin(5x)=−1
양쪽을 다음으로 나눕니다 333sin(5x)=3−1
단순화sin(5x)=−31
sin(5x)=−31
트리거 역속성 적용
sin(5x)=−31
일반 솔루션 sin(5x)=−31sin(x)=−a⇒x=arcsin(−a)+2πn,x=π+arcsin(a)+2πn5x=arcsin(−31)+2πn,5x=π+arcsin(31)+2πn
5x=arcsin(−31)+2πn,5x=π+arcsin(31)+2πn
5x=arcsin(−31)+2πn해결 :x=−5arcsin(31)+52πn
5x=arcsin(−31)+2πn
arcsin(−31)+2πn간소화하다 :−arcsin(31)+2πn
arcsin(−31)+2πn
다음 속성을 사용하십시오: arcsin(−x)=−arcsin(x)arcsin(−31)=−arcsin(31)=−arcsin(31)+2πn
5x=−arcsin(31)+2πn
양쪽을 다음으로 나눕니다 5
5x=−arcsin(31)+2πn
양쪽을 다음으로 나눕니다 555x=−5arcsin(31)+52πn
단순화x=−5arcsin(31)+52πn
x=−5arcsin(31)+52πn
5x=π+arcsin(31)+2πn해결 :x=5π+5arcsin(31)+52πn
5x=π+arcsin(31)+2πn
양쪽을 다음으로 나눕니다 5
5x=π+arcsin(31)+2πn
양쪽을 다음으로 나눕니다 555x=5π+5arcsin(31)+52πn
단순화x=5π+5arcsin(31)+52πn
x=5π+5arcsin(31)+52πn
x=−5arcsin(31)+52πn,x=5π+5arcsin(31)+52πn
범위에 맞는 솔루션 x<2πx=−5arcsin(31),x=5π+arcsin(31),x=5−arcsin(31)+2π,x=53π+arcsin(31),x=5−arcsin(31)+4π,x=55π+arcsin(31),x=5−arcsin(31)+6π,x=57π+arcsin(31),x=5−arcsin(31)+8π,x=59π+arcsin(31),x=5−arcsin(31)−2π,x=5−π+arcsin(31),x=5−arcsin(31)−4π,x=5−3π+arcsin(31),x=5−arcsin(31)−6π,x=5−5π+arcsin(31),x=5−arcsin(31)−8π,x=5−7π+arcsin(31)
해를 10진수 형식으로 표시x=−50.33983…,x=5π+0.33983…,x=5−0.33983…+2π,x=53π+0.33983…,x=5−0.33983…+4π,x=55π+0.33983…,x=5−0.33983…+6π,x=57π+0.33983…,x=5−0.33983…+8π,x=59π+0.33983…,x=5−0.33983…−2π,x=5−π+0.33983…,x=5−0.33983…−4π,x=5−3π+0.33983…,x=5−0.33983…−6π,x=5−5π+0.33983…,x=5−0.33983…−8π,x=5−7π+0.33983…