數學 help

1. 180° ≦ x ≦ 360°. 解 5 sinx － 3cosx ＝ 0
Sol:
5 sinx － 3cosx ＝ 0
5 sinx ＝ 3cosx
25 sin²x = 9 cos²x
25 sin²x ＝ 9 ( 1 － sin²x )
34 sin²x ＝ 9
sin²x ＝ 9/34
sinx ＝ ± √(9/34) ( 180° ≦ x ≦ 360°, x ＝ √(9/34) rejected )
sinx ＝ - √(9/34)
x ＝ 329.04° or 210.96°
x ＝ 329.04° 帶入原式不合 ( rejected )
x ＝ 210.96°
Ans: x ＝ 210.96°
2. siny ＋ 1 及 cosy ＋ 1 是 x² － 2x ＋ k ＝ 0的根, k ＝
Sol:
by α ＋ β ＝ - b/a
( siny ＋ 1 ) ＋ ( cosy ＋ 1 ) ＝ - ( - 2/1 )
siny ＋ cosy ＋ 2 ＝ 2
siny ＋ cosy ＝ 0
sin²y ＋ 2 siny cosy ＋ cos²y ＝ 0 ( square both sides )
2 siny cosy ＋ 1 ＝ 0
siny cosy ＝ - 1/2
also by αβ ＝ c/a
( siny ＋ 1 ) ( cosy ＋ 1 ) ＝ k/1
siny cosy ＋ siny ＋ cosy ＋ 1 ＝ k
- 1/2 ＋ 0 ＋ 1 ＝ k
k ＝ 1/2
Ans: k ＝ 1/2

1.
5sin(x)-3cos(x)=0
5tan(x)-3=0
tan(x)=3/5 (180<=x<=360)
x=tan-1(3/5)+k*180 (k=1)
=30.964+180
=210.964 degrees

2.
x² － 2x ＋ k ＝ 0
x=2+/-((-2)^2-4k)/2
=1+/-2sqrt(1-k)
Therefore
sin(x)=sqrt(1-k)
cos(x)=-sqrt(1-k)
or sin(x)=-cos(x)
x=3pi/4
sin(3pi/4)=sqrt(1/2)
sqrt(1/2)=sqrt(1-k)
k=1-1/2=1/2