Expert: Socrates - 1/21/2009

Question
Evaluate all six trigonometric functions at t, where the given point lies on the terminal side of an angle of t radians in standard position. (If there is no answer, enter NONE in the answer box.)
(3, 0)

sin(t) =    

cos(t) =    

tan(t) =    

csc(t) =    

sec(t) =    

cot(t) =

Answer
If (x,y) are the coordinates of a point on the terminal side of an angle t , then

sin(t) = y / (x^2 + y^2)^1/2

cos(t) = x / (x^2 + y^2)^1/2

tan(t) = y/x

csc(t) = 1/sin(t)

sec(t) = 1/cos(t)

cot(t) = 1/tan(t)


Just plug in x = 3 and y = 0 for the point (3,0)

sin(t) = 0

cos(t) = 1

tan(t) = 0

csc(t) undefined

sec(t) = 1

cot(t) undefined