Question

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

Answer 1

Answer: a

Step-by-step explanation: edge 2021

Answer 2

cos∅=-
`(√(85) )/(11)`

tan∅ -
`-(6√(85) )/(85)`

Explanation:

sin∅ =
`(6)/(11)`

we know that

cos∅ =
`√(1-sin^2∅  )`

plugging the value of sin∅ gives

`\sqrt{ 1-((6)/(11))^2\sqrt{ 1-((36)/(121))\\\sqrt{(85)/(121) } \\(√(85) )/(11\\)`

therefore cos∅=-
`(√(85) )/(11)`

cos∅ is negative since sec∅ is negative

tan∅ =
`(sin∅)/(cos∅)`

=
`\frac{(6)/(11) }{\frac{\-sqrt{85}  }{11} } \\`

on simplifying it ,we get

=-
`(6)/(√(85) )`

rationalizing it we get

-
`-(6√(85) )/(85)`