Solve giving values of theta from 0 to 360 degrees inclusive
1. 2sinx-cosecx=1
2. 2 tan(theta/2)+ 3 tan theta=0
Solve giving values of x from 0 to 2 pi inclusive:
1. tan2theta+ tantheta=0
2. 2cosec2theta=1 + tan^2
thanks if you can help
Solve giving values of theta from 0 to 360 degrees inclusive
1. 2sinx-cosecx=1
2. 2 tan(theta/2)+ 3 tan theta=0
Solve giving values of x from 0 to 2 pi inclusive:
1. tan2theta+ tantheta=0
2. 2cosec2theta=1 + tan^2
thanks if you can help
Hello, Confuzzled!
Here's the first one . . .
Solve for 0° ≤ x ≤ 360°
1) .2·sin x - csc x .= .1
Multiply through by sin x: . 2·sin²x - 1 .= .sin x
We have: . 2·sin²x - sin x - 1 .= .0
which factors: . (sin x - 1)(2·sin x + 1) .= .0
and has these roots:
. . sin x - 1 .= .0 . →. sin x = 1 . → . x = 90°
. . 2·sinx + 1 .= .0 . → . sin x = -½ . → . x .= .210°, 330°
2) .2·tan(x/2)+ 3 tan x .= .0
Using a double-angle identity, we have:
. . . . . . . . . . . . . .2·tan(x/2)
. . 2·tan(x/2) + 3 ---------------- .= .0
. . . . . . . . . . . . .1 - tan²(x/2)
This simplifies to: .2·tan³(x/2) - 8·tan(x/2) .= .0
which factors: . 2·tan(x/2) [tan²(x/2) - 4] .= .0
and has these roots:
. . 2·tan(x/2) = 0 . → . x/2 .= .0°, 180° . → . x .= .0°, 360°
. . tan²(x/2) = 4 . → . tan(x/2) = ±2 . → . x. = .2·arctan(±2) .≈ .126.9°, 233.1°