Graphing Trigonometric Functions with Domain and Range
Key Questions

Answer:
Using a graphing calculator: MODE must be in radians
Explanation:
Using a graphing calculator: MODE must be in radians.
On a TI graphing calculator, with the standard zoom,
#Y1 = sin(x)# :graph{sin(x) [10.04, 9.96, 5.16, 4.84]}
On a TI graphing calculator, with the standard zoom,
#Y1 = cos(x)# :graph{cosx [10.04, 9.96, 5.16, 4.84]}
On a TI graphing calculator, with the standard zoom,
#Y1 = tan(x)# :graph{tan x [10.04, 9.96, 5.16, 4.84]}
On a TI graphing calculator, with the standard zoom,
#y = sec(x): Y1 = 1/(cos(x))# :graph{1/(cos x) [10.04, 9.96, 5.16, 4.84]}
On a TI graphing calculator, with the standard zoom,
#y = csc(x): Y1 = 1/(sin(x))# :graph{1/(sin x) [10.04, 9.96, 5.16, 4.84]}
On a TI graphing calculator, with the standard zoom,
#y = cot(x): Y1 = 1/(tan(x))# :graph{1/(tan x) [10.04, 9.96, 5.16, 4.84]}

Answer:
#sin(x)# ,#cos(x)# ,#tan(x)# ,#csc(x)# ,#sec(x)# ,#cot(x)# .Explanation:
#cos(x)=sin(pi/2x)# #tan(x)=frac{sin(x)}{cos(x)}# #csc(x)=1/sin(x)# #sec(x)=1/cos(x)# #cot(x)=1/tan(x)# 
Given a right triangle, select a vertex where the hypotenuse and one of the legs meet.
The angle
#theta# created by this two sides will be used as a reference pointThe side that formed the angle
#theta# together with the hypotenuse will be referred to as#adjacent# (side adjacent to the angle). The other side will be referred to as#opposite# (side opposite the angle)The ratio between the
#opposite# and the#"hypotenuse"# is called#"sine" (sin# ). The inverse of this ratio is called#"cosecant" (csc# )#sin theta = "opposite" / "hypotenuse" # #csc theta = "hypotenuse" / "opposite" = 1 / sin theta# The ratio between the
#adjacent# and the#"hypotenuse"# is called "cosine". The inverse of this ratio is called "secant"#cos theta = "adjacent" / "hypotenuse" # #sec theta = "hypotenuse" / "adjacent" = 1 / cos theta# The ratio between the
#opposite# and the#adjacent# is called
#"tangent"# . The inverse of this ratio is called#"cotangent"# #tan theta = "opposite" / "adjacent"# #cot theta = "adjacent" / "opposite" = 1 / tan theta#
For example, in a 306090 triangle
#sin 30 = 1 / 2#
#cos 30 = 3^(1/2)/2#
#tan 30 = 1 / 3^(1/2)#
#csc 30 = 2#
#sec 30 = 2/3^(1/2)#
#cot 30 = 3^(1/2)# #sin 60 = 3^(1/2)/2#
#cos 60 = 1 /2 #
#tan 60 = 3^(1/2)#
#csc 60 = 2/3^(1/2)#
#sec 60 = 2#
#cot 60 = 1 / 3^(1/2)#