Determine the values of the trigonometric functions of angle a if P is a point on terminal side of a .The coordinates of P are (3,4); (-3,4);...

We know that the definitions of the trigonometric
functions are:

sin a = y/r

cos
a = x/r

tan a = y/x

cot a =
x/y

sec a = r/x

csc a =
r/y

We'll calculate r using the Pythagorean theorem in a
right angle triangle:

r^2 = x^2 +
y^2

r = sqrt (x^2 + y^2)

We'll
calculate the values for the trigonometric functions and we'll choose the smallest
positive angle in the standard position for P(3,4).

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

r =
sqrt(9+16)

r = sqrt 25

r =
5

sin a = 4/5 ; cos a =
3/5

tan a = sin a/cos a

tan a
= (4/5)/(3/5)

tan a = 4/3

cot
a = 1/tan a

cot a = 3/4

sec a
= 5/3

csc a = 5/4

We'll
calculate the values for the trigonometric functions and we'll choose the smallest
positive angle in the standard position for P(-3,4).

r =
sqrt [(-3)^2 + 4^2]

r =
sqrt(9+16)

r = sqrt 25

r =
5

sin a = 4/5 ; cos a =
-3/5

tan a = sin a/cos a

tan a
= (4/5)/(-3/5)

tan a =
-4/3

cot a = 1/tan a

cot a =
-3/4

sec a = -5/3

csc a =
5/4

We'll calculate the values for the trigonometric
functions and we'll choose the smallest positive angle in the standard position for
P(-1,-3).

r = sqrt [(-1)^2 +
(-3)^2]

r = sqrt(1+9)

r = sqrt
10

sin a = -3/sqrt10

sin a =
-3*sqrt10/10

cos a =
-1/sqrt10

cos a =
-sqrt10/10

tan a =
(-3*sqrt10/10)/( -sqrt10/10)

tan a =
3

cot a = 1/3

sec a =
-sqrt10

csc a = -sqrt10/3