SOLUTION: The terminal side of an angle θ (theta) in standard position passes through the point (3,-6). Find the values of all six trigonometric function. Rationalize all denominators.

Algebra ->  Angles -> SOLUTION: The terminal side of an angle θ (theta) in standard position passes through the point (3,-6). Find the values of all six trigonometric function. Rationalize all denominators.      Log On


   

Question 1108655: The terminal side of an angle θ (theta) in standard position passes through the point (3,-6). Find the values of all six trigonometric function. Rationalize all denominators.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the terminal side of angle theta , in standard position,
passes through P%28x%5BP%5D%2Cy%5BP%5D%29
tan%28theta%29%22=%22y%5BP%5D%2Fx%5BP%5D ; cot%28theta%29%22=%22x%5BP%5D%2Fy%5BP%5D ;
sin%28theta%29%22=%22y%5BP%5D%2Fsqrt%28x%5BP%5D%5E2%2By%5BP%5D%5E2%29 ; cos%28theta%29%22=%22x%5BP%5D%2Fsqrt%28x%5BP%5D%5E2%2By%5BP%5D%5E2%29 ;
sec%28theta%29%22=%22%28cos%28theta%29%29%5E%28-1%29 , and csc%28theta%29%22=%22%28sin%28theta%29%29%5E%28-1%29 .

So, in this case,
tan%28theta%29%22=%22-6%2F3%22=%22-2 ; cot%28theta%29%22=%223%2F%28-6%29%22=%22-1%2F2 ;
sin%28theta%29%22=%22%28-6%29%2Fsqrt%283%5E2%2B%28-6%29%5E2%29%22=%22%28-6%29%2Fsqrt%289%2B36%29+%22=%22%28-6%29%2Fsqrt%2845%29%22=%22%28-6%29%2F3sqrt%285%29%22=%22-2%2Fsqrt%285%29%22=%22-2sqrt%285%29%2F5 ;
cos%28theta%29%22=%223%2Fsqrt%283%5E2%2B%28-6%29%5E2%29%22=%223%2Fsqrt%289%2B36%29+%22=%223%2Fsqrt%2845%29%22=%223%2F3sqrt%285%29%22=%221%2Fsqrt%285%29%22=%22sqrt%285%29%2F5 ;
sec%28theta%29%22=%22%281%2Fsqrt%285%29%29%5E%28-1%29%22=%22sqrt%285%29 , and
csc%28theta%29%22=%22%28-2%2Fsqrt%285%29%29%5E%28-1%29%22=%22-sqrt%285%29%2F2 .