The Unit Circle
1) You are given the coordinate of (5,-12). Use the Pythagorean theorem to find the hypotenuse and then find the sin,cos,csc,sec,tan and cot.
*create a coordinate grid.
*since your first coordinate is a 5 you will want to move 5 over to the right.
*since your second coordinate is -12 you will want to move down 12
*create a right triangle between these points
*to find the hypotenuse you will want to use the Pythagorean theorem
*this is a squared + b squared
* 5=a and -12=b
*5 squared=25 and -12 squared=144
*add them together to get 169
*take the square root of that to get 13, 13 is the hypotenuse or r
*sin is y/r so it is -12/13
*cos is x/r so it is 5/13
*tan is y/x so it is -12/5
*csc is r/y so it is -13/12
*sec is r/x so it is 13/5
*cot is x/y so it is -5/12

2) You are given Cos=8/17 and are asked to find sin,csc,sec,tan, and cot
*first you know that cos is x/r
*that would mean that x=8 and r=17
*use the Pythagorean theorem to find y
*set up the equation as 8 squared + y squared=17 squared
*do the math and you would have 64+y squared=289
*subtract 64 from both sides
*this would leave you with y squared =225
*you would then square root both sides
*this would leave you with y=15
*sin is y/r so it is 15/17
*csc is r/y so it would be 17/15
*sec is r/x so it would be 17/8
*tan is y/x so it would be 15/8
*cot is x/y so it would be 8/15

3) You are give Sin=-3/4 and Tan is less than 0. Find X= look at the answer section under "more"