Question

Find the general values of `theta` from the following equations:
i) `sin^(2)theta=3/4`
ii) `cos^(2)theta=1/2`
iii) `tan^(2)theta=1/3`

Answer 1

i) `sin^(2)theta=3/4=(sqrt(3)/2)^(2)`
`=sin^(2)pi/3`
`therefore theta=nx+-pi/3`.
ii) `cos^(2)theta=1/2=(1/sqrt(2))^(2)`
`=cos^(2)pi/4`
`therefore theta=npi+-pi/4` Ans.
iii) `tan^(2)theta=1/3`
`=(1/sqrt(3))^(2)=tan^(2)pi/6`
`therefore theta=npi+-pi/6`. Ans.