Question

Given sintheta=6/11 and sectheta<0 find costheta and tan theta

Answer 1

Answer:

cos∅=-$\frac{\sqrt{85} }{11}$

tan∅ -$-\frac{6\sqrt{85} }{85}$

Step-by-step explanation:

sin∅ =$\frac{6}{11}$

we know that

cos∅  =$\sqrt{1-sin^2∅ }$

plugging the value of sin∅  gives

$\sqrt{ 1-(\frac{6}{11})^2\sqrt{ 1-(\frac{36}{121})\\\sqrt{\frac{85}{121} } \\\frac{\sqrt{85} }{11\\}$

therefore  cos∅=-$\frac{\sqrt{85} }{11}$

cos∅  is negative since sec∅  is negative

tan∅ =  $\frac{sin∅}{cos∅}$

           =$\frac{\frac{6}{11} }{\frac{\-sqrt{85} }{11} }$

            on simplifying it ,we get

    =-$\frac{6}{\sqrt{85} }$

rationalizing it we get

-$-\frac{6\sqrt{85} }{85}$