Relative Position of a Point with Respect to a Line
sin θ, cos θ ...
Question
(sinθ,cosθ) and (3,2) lies on the same side of the line x+y=1, then θ lies between
A
(0,π2)
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B
(0,π)
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C
(π4,π2)
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D
(0,π4)
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Solution
The correct option is D(0,π4) As (sinθ,cosθ) and (3, 2) lie on the same side of x+y-1=0 , they should be of same sign. ∴sinθ+cosθ−1>as3+2−1>0 ⇒√2sin(θ+π4)>1 ⇒sin(θ+π4)>1√2⇒0<θ<π4.