Question

Please help me right away.

Answer 1

Look at the picture.

Definitions:

`\sin\theta=(y)/(r)\\\\\cos\theta=(x)/(r)\\\\\tan\theta=(y)/(x)\\\\\cot\theta=(x)/(y)`

We have:

`\sin\theta=(5)/(6)` and Quadrant II (x < 0, y > 0)

Therefore y = 5 and r = 6. Calculate x:

`r=√(x^2+y^2)\to√(x^2+5^2)=6\ \ \ |^2\\\\x^2+25=36\ \ \ |-25\\\\x^2=11\to x=-√(11)`

Sunstitute to the formula of tan:

`\tan\theta=(5)/(-√(11))=-(5)/(√(11))\cdot(√(11))/(√(11))=-(5√(11))/(11)`

Answer: d.