Question

Find the values of the six trigonometric functions for angle θ in standard position if a point with the coordinates (-3,-5) lies on its terminal side.

Answer 1

In this case:

x = - 3 , y = - 5

r = √ ( x² + y² )

r = √ [ ( - 3 )² + (- 5 )² ]

r = √ ( 9 + 25 )

r = √34

sin θ = y / r = - 5 / √34

cos θ = x / r = - 2 / √34

sec θ = 1 / cos θ = - √34 / 2

csc θ = 1 / sin θ = - √34 / 5

tan θ = sin θ / cos θ = ( - 5 / √34 ) / ( - 2 / √34 ) = 5 / 2

cot θ = cos θ / sin θ = ( - 2 / √34 ) / ( - 5 / √34 ) = 2 / 5