Question

Given 2cos3 theta = root 3 find the value of theta

Answer 1

2cos 3theeta=√3
cos3 theeta =√3/2
cos3theeta=cos 30
compare to both side
3 theeta =30
theeta=30/3
(theeta=10)
putting the value of theeta in 1st equation
2cos3×10=√3
2cos30=√3
2×√3/2=√3
√3=√3
LHS=RHS

Answer 2

Answer:

The value of theta will be 10° in the first quadrant.

$\theta = \frac{π}{18} = 10°$

Step-by-step explanation:

Given that

$2 \cos( 3\theta ) = \sqrt{3}$

Simplying it ,

$\cos( 3\theta ) = \frac{ \sqrt{3} }{2}$

Now we know that Cos30° = √3/2 in the first quadrant.

therefore

$3\theta = \cos ^{ - 1}( \frac{ \sqrt{3} }{2} ) = \frac{\pi}{6}$

In the first Quadrant the value of theta will be

$3\theta = \frac{π}{6} = 30°$

$\theta = \frac{π}{18} = 10°$

General Solution:

Cosx have positive values in first and fourth quadrant. It is a periodic function and repeat it's value after every 2π angle. It has equal values in first and fourth quadrant.

$3 \theta = 2n\pi \pm \frac{\pi}{6}$

where n belongs to set of integers i.e. Z

Therefore

$\theta = 2n\pi \pm \frac{\pi}{18}$

where n belongs to set of integers Z