Find the exact values of the six trigonometric functions of

Find the exact values of the six trigonometric functions of if is in standard position and the terminal side of is in the specified quadrant and satisfies the given condition.

III; parallel to the line 5y 3x + 5 = 0

sin =_____

cos =____

tan =_____

csc =______

sec =______

cot =______

Solution

Solution\"

is lying in III quadrant

and parallel to 5y-3x=5

therefore slope y =3x/5 +5/5

slope = 3/5

since terminal side is parallel to given line therefore slope of terminal equal = 3/5

= tan^-1( 3/5) = 30.96

and moreover

tan() = 3/5

Base = 5 and height = 3 and hypotenuse = (5² +3²) = 34

Hence In third quardant

sin =-3/34 = -0.51

cos =-5/34 = -0.86

tan = 3/5

csc = -34 /3= -1.94

sec = -34 /5 = -1.16

cot =5/3 = 1.67