Let P(x, y) be a point on the unit circle such that the radius OP forms an angle of 𝜃 radians with respect to the positive x-axis.

Question

Fill in the blank.

Let P(x, y)

 be a point on the unit circle such that the radius OP forms an angle of 𝜃 radians with respect to the positive x-axis.

Write an equation that defines each of the following trigonometric functions of 𝜃 in terms of x and y.

sin 𝜃	=				csc 𝜃	=
cos 𝜃	=				sec 𝜃	=
tan 𝜃	=				cot 𝜃	=

Answer 1

tanT = y/x

cotT = 1/tanT = x/y

sinT = y/(sqr(x^2+y^2))

cscT = 1/sinT = (sqr(x^2+y^2))/y

cosT = x/(sqr(x^2+y^2))

secT =1/cosT = (sqr(x^2+y^2))/x