Question

Please help me with this right away. Please show the work

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:

`\tan\theta=-(2)/(3)` and Quadrant II (x < 0, y > 0)

Therefore x=-3 and y = 2. Calculate r:

`r=√((-3)^2+2^2)=√(9+4)=√(13)`

Substitute to the formula of cosine:

`\cos\theta=(-3)/(√(13))=-(3)/(√(13))\cdot(√(13))/(√(13))=-(3√(13))/(13)`

Answer: a.