We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

#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