In Exercises 1724 a point on the terminal side of an angle i

In Exercises 17-24, a point on the terminal side of an angle is given. Find the exact values of the six trigonometric functions of . 17. (-4, 3) 19. (-V3,-1) 21. (3,3) 23. (12,-5) 18. (-3,5) 22. (-2,-2) 24. (7,-2)

Solution

17) ( - 4 , 3 )

finding r

r = sqrt ( 4^2 + 3^2 ) = 5

sin theta = y/r = 3 / 5

cos theta = x / r = - 4 / 5

tan theta = sin theta / cos theta = - 3 / 4

csc theta = 1/ sin theta = 5/3

sec theta = 1 / cos theta = -5/4

cot theta = 1/ tan theta = - 4 / 3

18) ( -3 . 5 )

finding r

r = sqrt ( 3^2 + 5^2 ) = sqrt 34

sin theta = y/r = 5 / sqrt 34 = 5 sqrt 34 / 34

cos theta = x / r = - 3 / sqrt 34 = - 3 sqrt 34 / 34

tan theta = - 5 /3

csc theta = 1 / sin theta = sqrt 34 / 5

sec theta = 1 / cos theta = - sqrt 34 / 3

cot theta = 1 / tan theta = - 3/5