해법
cos2(111∘)+cos2(69.3∘)+cos2(x)=1
해법
x=0.52748…+360∘n,x=360∘−0.52748…+360∘n,x=2.61410…+360∘n,x=−2.61410…+360∘n
+1
라디안
x=0.52748…+2πn,x=2π−0.52748…+2πn,x=2.61410…+2πn,x=−2.61410…+2πn솔루션 단계
cos2(111∘)+cos2(69.3∘)+cos2(x)=1
대체로 해결
cos2(111∘)+cos2(69.3∘)+cos2(x)=1
하게: cos(x)=ucos2(111∘)+cos2(69.3∘)+u2=1
cos2(111∘)+cos2(69.3∘)+u2=1:u=1−cos2(111∘)−cos2(69.3∘),u=−1−cos2(111∘)−cos2(69.3∘)
cos2(111∘)+cos2(69.3∘)+u2=1
cos2(111∘)를 오른쪽으로 이동
cos2(111∘)+cos2(69.3∘)+u2=1
빼다 cos2(111∘) 양쪽에서cos2(111∘)+cos2(69.3∘)+u2−cos2(111∘)=1−cos2(111∘)
단순화cos2(69.3∘)+u2=1−cos2(111∘)
cos2(69.3∘)+u2=1−cos2(111∘)
cos2(69.3∘)를 오른쪽으로 이동
cos2(69.3∘)+u2=1−cos2(111∘)
빼다 cos2(69.3∘) 양쪽에서cos2(69.3∘)+u2−cos2(69.3∘)=1−cos2(111∘)−cos2(69.3∘)
단순화u2=1−cos2(111∘)−cos2(69.3∘)
u2=1−cos2(111∘)−cos2(69.3∘)
위해서 x2=f(a) 해결책은 x=f(a),−f(a)
u=1−cos2(111∘)−cos2(69.3∘),u=−1−cos2(111∘)−cos2(69.3∘)
뒤로 대체 u=cos(x)cos(x)=1−cos2(111∘)−cos2(69.3∘),cos(x)=−1−cos2(111∘)−cos2(69.3∘)
cos(x)=1−cos2(111∘)−cos2(69.3∘),cos(x)=−1−cos2(111∘)−cos2(69.3∘)
cos(x)=1−cos2(111∘)−cos2(69.3∘):x=arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n,x=360∘−arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n
cos(x)=1−cos2(111∘)−cos2(69.3∘)
트리거 역속성 적용
cos(x)=1−cos2(111∘)−cos2(69.3∘)
일반 솔루션 cos(x)=1−cos2(111∘)−cos2(69.3∘)cos(x)=a⇒x=arccos(a)+360∘n,x=360∘−arccos(a)+360∘nx=arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n,x=360∘−arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n
x=arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n,x=360∘−arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n
cos(x)=−1−cos2(111∘)−cos2(69.3∘):x=arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n,x=−arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n
cos(x)=−1−cos2(111∘)−cos2(69.3∘)
트리거 역속성 적용
cos(x)=−1−cos2(111∘)−cos2(69.3∘)
일반 솔루션 cos(x)=−1−cos2(111∘)−cos2(69.3∘)cos(x)=−a⇒x=arccos(−a)+360∘n,x=−arccos(−a)+360∘nx=arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n,x=−arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n
x=arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n,x=−arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n
모든 솔루션 결합x=arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n,x=360∘−arccos(1−cos2(111∘)−cos2(69.3∘))+360∘n,x=arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n,x=−arccos(−1−cos2(111∘)−cos2(69.3∘))+360∘n
해를 10진수 형식으로 표시x=0.52748…+360∘n,x=360∘−0.52748…+360∘n,x=2.61410…+360∘n,x=−2.61410…+360∘n