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If cottheta=5//12andtheta lies in the third quadrant , then what is (2sintheta+3costheta) equal to? |
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Answer» `-4` `rArrtantheta=(12)/(5)=("perpendicular"(P))/("base"(b))` `therefore"Hypotenuse"(H)=sqrt(p^(2)+b^(2))` `=sqrt((12)^(2)+(5)^(2))=sqrt(144+255)=sqrt(169)=13` Consider 2 `2sintheta+3costheta` `=2((p)/(H))+3((b)/(H))`""(H- Height) But`theta`lies in `3^(rd)`QUADRANT and sin `theta , costheta` both are negative in `3^(rd)` quadrant `therefore2sintheta+3costheta=2((-p)/(H))+3((-b)/(H))` `=2((-12)/(13))+3((-5)/(13))` `=(-24-15)/(13)=(-39)/(13)=-3` WHICHIS an odd prime. |
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