Maths Trigonometry 20 pts

1. Solve 3tanx-2=0 for -180<x<180
tanx = 2/3
x = 33.69
for -180<x<180 ,
x = 33.69° or 33.69 - 180 = -146.31°
2. 2sin^2x-sinx-1=0 for -180<x<180
(2sinx + 1)(sinx - 1) = 0
sinx = - 1/2 or sinx = 1
x = - 30° or 180 - (-30) = 210°(rejected), or x = 90° , for -180<x<180
3.Prove that (sinx+cosx)^2 = 1+2sinx cosx
LHS = (sinx)^2 + 2sinx cosx + (cosx)^2
= 1 + 2sinx cosx = RHS
4. Prove that 1/ cosx - cosx= sinx tanx ,cosx not equal to 0
LHS =
1 / cosx - (cosx)^2 / cosx
= [(1 - (cosx)^2 ] / cosx
= (sinx)^2 / cosx
= (sinx) (sinx / cosx)
= sinx tanx
= RHS

2010-04-09 22:40:39 補充：
Corr :

2. 2sin^2x-sinx-1=0 for -180<180

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

sinx = - 1/2 or sinx = 1

x = - 30° or 180 - (-30) = 210° = 360 - 210 = - 150°, or x = 90° , for -180<180

2010-04-09 22:43:58 補充：
210 - 360 = - 150°

2010-04-09 22:54:49 補充：
Other method :

For sinx = - 1/2 ,

x = 210° or 330° , for 0° <= x <= 360°

so

x = 210 - 360 = - 150° or 330 - 360 = - 30° for - 180° < x < 180°

For sinx = 1 ,

x = 90° for - 180° < x < 180°


x = - 150° , - 30° , 90°