tan θ = xyx ≠ 0 cot θ = yxy ≠ 0 reciprocal of sin θ

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          Finding  All  Six  Trigonometric  Values  Given  One  (x,y)  Point          

   

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Let ! be an angle in standard position and P(x,y) lie on the terminal side of ! a distance of r from the origin such that r = x2 + y2, then...

sin ! =

y r

csc ! =

r y

y≠0

reciprocal of sin !

cos ! =

x r

sec ! =

r x

x≠0

reciprocal of cos !

tan ! =

y x

cot ! =

x y

y≠0

reciprocal of tan !

x≠0

 

         

Let (-4,3) lie on the terminal side of ! in standard position. Find all six trig values of !.

(-4,3) r

y sin ! = r

   

r csc ! = y

cos ! =

x r

sec ! =

r x

tan ! =

y x

cot ! =

x y

!

 

     

Let (5,-12) lie on the terminal side of ! in standard position. Find all six trig values of !.

sin ! =

y r

csc ! =

r y

cos ! =

x r

sec ! =

r x

tan ! =

y x

cot ! =

x y

! r

(5,-12)  

           

Let (2,3) lie on the terminal side of ! in standard position. Find all six trig values of !. (2,3) r

     

sin ! =

y r

csc ! =

r y

cos ! =

x r

sec ! =

r x

tan ! =

y x

cot ! =

x y

!

 

© iTutoring.com Finding  All  Six  Trigonometric  Values  Given  One  (x,y)  Point     Pg.  2  

   

Let (-6,-6) lie on the terminal side of ! in standard position. Find all six trig values of !.

sin ! =

y r

csc ! =

r y

cos ! =

x r

sec ! =

r x

y x

cot ! =

tan ! =

! r (-6,-6)

x y  

             

Let ! be an angle in standard position and P(x,y) lie on the terminal side of ! a distance of r from the origin such that r = x2 + y2, then...

     

sin ! =

y r

csc ! =

r y

y≠0

reciprocal of sin !

cos ! =

x r

sec ! =

r x

x≠0

reciprocal of cos !

tan ! =

y x

cot ! =

x y

y≠0

reciprocal of tan !

x≠0

 

© iTutoring.com Finding  All  Six  Trigonometric  Values  Given  One  (x,y)  Point     Pg.  3