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schepotkina [342]
3 years ago
15

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

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
5 0

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}

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