中4數學題

1.
3cos x - 5sin x = -cos x + sin x
4cosx-6sinx=0
6sinx=4cosx
6tanx=4
tanx=2/3
x=33.69,213.69

2.
tan^2x = 3
tanx=√3or-√3
x=60,240or120,300

3.
cos^2x - sin^2x = -sin x
1-2sin^2x+sinx=0
2sin^2x-sinx+1=0
(2sinx+1)(sinx-1)=0
sinx=-0.5or1
x=210,330or90

4.
6sin^2x - sin x cos x - 2cos^2x=0
6tan^2x-tanx-2=0
(3tanx-2)(2tanx+1)
tanx=2/3or-0.5
x=33.69,213.69or153.43,333.43

Solve the following equations for 0 ≦ x ≦360

1.
3cos x - 5sin x = -cos x + sin x

4cosx = 6sinx

tanx = 2/3

x = tan^-1(2/3) or x = 180 + tan^-1(2/3)


2.
tan^2x = 3

tanx = (3)^0.5

x = 60 or 240



3.
cos^2x - sin^2x = -sin x

1 - 2sin^2x = -sinx

2sin^2x - sinx - 1 = 0

(2sinx + 1)(sinx - 1) = 0

sinx = -1/2 or sinx = 1

x = 210 or 330 or x = 90

x = 90,210,330



4.
Solve 6sin^2x - sin x cos x - 2cos^2x = 0 ≦ x ≦ 360

(3sinx - 2cosx)(2sinx + cosx) = 0

tanx = 2/3 or tanx = -1/2

x = tan^-1(2/3) or x = 180 + tan^-1(2/3) or x = tan^-1(-1/2) or x = 360 - tan^-1(2/3)