The range of values of `theta` in the interval `(0, pi)` such that the points (3,5) and `(sin theta , cos theta)` lie on the same side of the line `x+y-1=0`, isA. `0 lt theta lt (pi)/(4)`B. `0 lt theta lt (pi)/(2)`C. `0 lt theta lt pi`D. `(pi)/(4) lt theta lt (3pi)/(4)`

The range of values of `theta` in the interval `(0, pi)` such that the

1.	The range of values of `theta` in the interval `(0, pi)` such that the points (3,5) and `(sin theta , cos theta)` lie on the same side of the line `x+y-1=0`, isA. `0 lt theta lt (pi)/(4)`B. `0 lt theta lt (pi)/(2)`C. `0 lt theta lt pi`D. `(pi)/(4) lt theta lt (3pi)/(4)`
Answer» Correct Answer - B We have line x+y-1=0. Let L(x,y) = x+y-1. `therefore L(3,5) = 3+5-1=7 gt 0` For points (3,5) and `"sin" theta, "cos" theta)` to lie on the same side line x+y-1=0, we must have `L("cos" theta, "sin" theta) gt 0` `"or " "sin" theta + "cos" theta-1 gt 0` `"sin" ((pi)/(4)+ theta) gt (1)/(sqrt(2))` `(pi)/(4) lt (pi)/(4) + theta lt (3pi)/(4)` `0 lt theta lt (pi)/(2)`

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The range of values of `theta` in the interval `(0, pi)` such that the points (3,5) and `(sin theta , cos theta)` lie on the same side of the line `x+y-1=0`, isA. `0 lt theta lt (pi)/(4)`B. `0 lt theta lt (pi)/(2)`C. `0 lt theta lt pi`D. `(pi)/(4) lt theta lt (3pi)/(4)`

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