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Find the range of 12sintheta-9sin^2theta...

Find the range of `12sintheta-9sin^2theta`

Text Solution

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The correct Answer is:
[-21, 4]
`f(x)=12sintheta-9sin^2theta`
`=-(9sin^2theta-12sintheta)`
`=-(9sin^2theta-12sintheta+4-4)`
`=-((3sintheta-2)^2-4)=4-(3sintheta-2)^2`
Minimum value of `f(theta)` occurs when `(3sintheta-2)^2` is minimum, which is 0.
Hence, range of `f(theta)` is `[4-25,4]-=[-21,4]`.
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