निम्नलिखित समीकरणों से `theta`के व्यापक मान ज्ञात कीजिए ।
(i) `sin^(3) 3 theta = 0 " "(ii) sin theta = -1`
(iii) `cot^(2) k theta = 0" "(iv) cos 5 theta = - 1/2`

Explanation

दिया है - `sin^(3) 3 theta = 0`
`rArr sin 3 theta = 0`
`rArr 3 theta = n pi, n in Z`
`:. theta = (n pi)/3 , n in Z`
(ii)दिया है - `sin theta = - 1 = sin (-pi/2)`
`rArr theta = n pi + (-1)^(n) (-pi/2)`
`rArr theta = n pi + (-1)^(n+1) * pi/2 , n in Z`
(iii) दिया है - `cot^(2) ktheta = 0`
`rArr cot k theta = 0`
`rArr (cos k theta)/(sin k theta) = 0`
`rArr cos k theta = 0`
`:. k theta = (2n+1) pi/2, n in Z`
`rArr theta = (2n+1). pi/(2k) , n in Z`
(iv) दिया है - `cos 5 theta = (-1)/2 = cos. (2pi)/3`
`rArr 5 theta = 2 n pi pm (2pi)/3, n in Z`
`rArr theta = 1/5 (2n pi pm (2pi)/3) , n in Z`