Trig Graphs!
Graph y = sin(x) and y = csc(x) in different colors on Desmos. Change the “step” of the x-axis to
pi. What do you notice about the graphs?
Name three places where y = csc(x) has an asymptote.
Give the value of the sine graph at each point.
What is responsible for this? Consider the relationship between sin and csc.
Remember limits? What is the limit of y = csc(x) as x approaches 4𝜋 from the positive side?
Write it out in limit notation here:
y = cos(x) is graphed below. Draw what you expect y = sec(x) to look like. Check by graphing
both in Desmos.
Here’s y = tan(x). Why are there asymptotes at
𝜋 3𝜋 5𝜋
2
,
2
,
2
, etc? It may help to look at the unit
circle and consider how you would calculate tangent at these values.
Take a stab at graphing what you think the y = cot(x) graph might look like, given that
tan(x) = 1/cot(x). Next, graph both in Desmos and see how close you got.
What is the domain of the y = cot(x) graph? Describe it by listing any undefined values:
x≠
What is the range?
Graph y = sin(x) again. What is the period of this graph?
If y = sin(x) were shifted like to the left like this: y = sin(x + 2π), how would the graph look
different?
Is this statement true?
How do you know?
sin(𝜃 + 2𝜋) = sin 𝜃
What about this one? cos(𝜃 + 2𝜋) = cos 𝜃
Fill in the blanks to make these statements true:
tan(𝜃 + ____ ) = tan 𝜃
csc(𝜃 + ____ ) = csc 𝜃
sec(𝜃 + ____ ) = sec 𝜃
cot(𝜃 + ____ ) = cot 𝜃