Question

Smart people. Please click here. I attached a pic of the problem

Answer 1

Look at the picture.

`r=√(x^2+y^2)`

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

We have the point
`\left((8)/(17),\ (15)/(17)\right)\to x=(8)/(17),\ y=(15)/(17)`.

Calculate r:

`r=\sqrt{\left((8)/(17)\right)^2+\left((15)/(17)\right)^2}=\sqrt{(64)/(289)+(225)/(289)}=\sqrt{(289)/(289)}=\sqrt1=1`

`\sin\theta=((15)/(17))/(1)=(15)/(17)\\\\\cos\theta=((8)/(17))/(1)=(8)/(17)\\\\\tan\theta=((15)/(17))/((8)/(17))=(15)/(17):(8)/(17)=(15)/(17)\cdot(17)/(8)=(15)/(8)\\\\\cot\theta=((8)/(17))/((15)/(17))=(8)/(17):(15)/(17)=(8)/(17)\cdot(17)/(15)=(8)/(15)\\\\\sec\theta=(1)/((8)/(17))=1:(8)/(17)=(17)/(8)\\\\\csc\theta=(1)/((15)/(17))=1:(15)/(17)=(17)/(15)`