#2**+1 **

Thanks Alan,

I always think of the unit circle when I answer questions like this.

(cos(3x+1))^2=0

the cos of the angle is given by the x coordinate that it extends to on the unit circle.

x is zero on the y axis and this is when the angle is 90, 270, 450..... degrees (Alan's answer is in radians pi/2, 3pi/2, 5pi/2... radians )

so

\(3x+1 = \frac{\pi}{2} + k\pi \qquad \text{ where k is an integer}\\ 3x= \frac{\pi}{2} + k\pi -1\\ x= \frac{\pi}{6} + \frac{2k\pi}{6} -\frac{2}{6}\\ x= \frac{\pi-2+2k\pi}{6} \)

Melody
Oct 9, 2017

#3**+1 **

Solve for x:

cos^2(3 x + 1) = 0

Take the square root of both sides:

cos(3 x + 1) = 0

Take the inverse cosine of both sides:

3 x + 1 = π n + π/2 for n element Z

Subtract 1 from both sides:

3 x = -1 + π/2 + π n for n element Z

Divide both sides by 3:

**x = -1/3 + π/6 + (π n)/3 for n element Z**

Guest Oct 9, 2017