反三角函数注意事项sin(arccos33/65+arctan4/3)=12/13把arccos33/65设为a如何求出a=33/65

Question

反三角函数注意事项
sin(arccos33/65+arctan4/3)=12/13
把arccos33/65设为a如何求出a=33/65

Answer 1

令a = arccos33/65
则有,
cos a = 33/65,sin a = 56/65
令b = arctan4/3
则有,
tan b = 4/3,sin b = 4/5 ,cos b = 3/5
sin(arccos33/65+arctan4/3)
= sin(a+b)
= sin a cos b + cos a sin b
= (56/65)(3/5) + (33/65)(4/5)
= 300/325
= 12/13