Question

if cos 3x=-1 where 0°≤x≤360°,then value of x.

Answer 1

Cos 3x = -1 ------(i)



Cos 180° = -1 --------(ii)


From (i) and (ii)

cos 3x = cos 180°

3x =180°
x = 60°.



Therefore, the value of x is 60°.

Answer 2

Well Hey Mate +_+

(•) Trigonometric Equations :p

$\cos(3x) = - 1$

$= > \cos(3x) = \cos(\pi)$

$= > \cos(3x) - \cos(\pi) = 0$

$= > 2 \sin( \frac{3x + \pi}{2} ) \sin( \frac{3x - \pi}{2} ) = 0$

But either of them can be zero ✓✓

So,

$\frac{3x + \pi}{2} = n\pi\: or \: \frac{3x - \pi}{2} = n\pi$

$= > x = \frac{(2n + 1)\pi}{3}$

*where "n" can take all Integral Values ^_^

Now,

${0}^{0} \leqslant x \leqslant {360}^{0}$

$= > x = \frac{\pi}{3} , \pi, \frac{5\pi}{3} \: (in \: radians)$
or

$= > x = {60}^{0} , {180}^{0} , {300}^{0}$

✓✓✓ Enjoy yer day ✓✓✓