Expert: Chanda Walker - 3/17/2009

Question
i have a few questions
Find X
1. tan2x+1=0 2.Cos^2x=1 3.arcsin(3x+1=pi/3 4. 2sin^2x=1

Covert into approximate radians
50 degrees & -60 degrees

covert into degrees
2pi/5, 3, 5pi/6

Answer
tan(2x) + 1 = 0
tan(2x) = 0

tan = sin/cos and sin = 0 at 0, Pi, 2 Pi, n Pi

2x = 0
x = 0


(There are multiple answers for all of these. I'll write the other options as with n in the solution.  n is any INTEGER!)

2x = n Pi
x = n Pi/2

x = n Pi/2

Cos^2(2x) = 1

Cos(2x) = +/- 1

Cos = +/-1 at 0, Pi, 2 Pi, n Pi

2x = n Pi
x = n Pi/2

ArcSin(3x + 1) = Pi/3
3x + 1 = Sin(Pi/3)
3x + 1 = Sqrt(3)/2
3x = 1 + Sqrt(3)/2
x = 1/3 + Sqrt(3)/6


2 sin^2(x) = 1
sin^2(x) = 1/2
sin(x) = +/-  1/Sqrt(2) = +/- Sqrt(2)/2
x = Pi/4 + n Pi/2
x = (2n + 1) Pi/4

50 * Pi/180 = 5/18 Pi = .873 rad


-60 * Pi/180 = -Pi/3 = 1.047

2 Pi/5 * 180/Pi = 360 /5 = 72 deg

5 Pi/6 * 180/Pi =  5 * 30 = 150 deg

Let me know if I can help further!