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If sin theta = (1)/(2)cos theta, and 0 l...

If `sin theta = (1)/(2)cos theta`, and `0 le theta le (pi)/(2)`, the value of `(1)/(2)sin theta` is

A

`0.22`

B

`0.25`

C

`0.45`

D

`0.50`

Text Solution

Verified by Experts

The correct Answer is:
A
You could use the given equation `sin theta = (1)/(2) cos theta` to find `theta`, but that's not really necessary. You could re-express the given equation putting it all in terms of sin `theta` :
`sin theta = (1)/(2) cos theta`
`sin theta = (1)/(2) sqrt(1-sin^(2)theta)`
`(sin theta)^(2)=((1)/(2) sqrt(1-sin^(2)theta))^(2)`
`sin^(2)theta = (1)/(4)(1-sin^(2)theta)`
`4sin^(2)theta = 1-sin^(2)theta`
`5 sin^(2)theta = 1`
`sin^(2)theta = (1)/(5)`
`sin theta = sqrt((1)/(5))~~ 0.45`
`(1)/(2)sin theta ~~ 0.22`
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