We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

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Domain and Range of Trigonometric Functions

The domain of a function is the specific set of values that the independent variable in a function can take on. The range is the resulting values that the dependant variable can have as x varies throughout the domain.

Domain and range for sine and cosine functions

There are no restrictions on the domain of sine and cosine functions; therefore, their domain is such that x ∈ R. Notice, however, that the range for both y = sin(x) and y = cos(x) is between -1 and 1. Therefore, transformations of these functions in the form of shifts and stretches will affect the range but not the domain.

$graph of sin(x) and cos(x)$

The domain and range for tangent functions

Notice that y = tan(x) has vertical asymptotes at:

$\pm\frac{(2n+1)\pi}{2}$

Therefore, its domain is such that:

$x\neq\pm\frac{(2n+1)\pi}{2}$

However, its range is such at y ∈ R, because the function takes on all values of y. In this case, transformations will affect the domain but not the range.

$the graph of tangent function$

Example: Find the domain and range of y = cos(x) – 3

Solution:

Domain: x ∈ R

Range: - 4 ≤ y ≤ - 2, y ∈ R

Notice that the range is simply shifted down 3 units.

Example: Find the domain and range of y = 3 tan(x)

Solution:

Domain: x ∈ R

$x\neq\pm\frac{(2n+1)\pi}{2}$

Notice that the domain is the same as the domain for y = tan(x) because the graph was stretched vertically—which does not change where the vertical asymptotes occur.

Range: y ∈ R

Example 1:

Example 2: