Trigonometric Function

**Definition:**

The trigonometric functions are transendental functions based on the ratios of the the sides of a right triangle. They include sine, cosine, tangent, secant, cosect and cotangent. The graphs of trigonometric functions are periodic in nature due to their relationship to the unit circle.

Transformational Form of a Trig Function:

VS = Vertical Stretch, "the amplitude"

VT = Vertical Translation, "sinusoidal axis"

HS = Horizontal Stretch, HS = old period/new period

HT = Horizontal Translation, "start on x"

**Trigonometric Function Photos:**

Mr. Lee's Example Photo

Photo Description: These cups from Mr. Lee's kitchen look like a tangent function!

Originators: Daniel & Alex

Photo Description: Banner in Mr. Lee's classroom that has two right angle triangles.

Originator: Hanna L

Photo Description: The bread in the pan my mother baked looks like a sine function

Originator: Maryam

Photo Description: The function y=cosx+1 on the sky.

Origionators: Alec and Jonathan

Photo Description: These grass hills on the top of Citidel Hill look like a cosine function

Originators: Adam and Alison

Photo Description: A mirror in the Discovery Center resembles a sine function (y=sinx). The vertical line is the y axis and the horizontal line is the x axis.

Originators: Lynne and Matthew

Photo Description: Lines 11-12 of *Claire De Lune *by Debussy form a cosine function AND a tangent function.

Originators: Gabrielle and Ellen

Photo description: These sail boats in Cuba (the picture was taken last year on march break) demonstrate right angle triangles. The length of side "c" can be calulated using the pythagorean theorm (shown on the picture). Trigonometry can also be used to calculate the angles and other side lengths of these triangles if at least one angle and one side are known.

Originator: Erika

The plants at Crystal Crescent Beach branch off from each other in such a way as to make an isoceles triangle. This means that two of the three sides are equal, and split in half, this triangle becomes two smaller right angle triangles.

Originators: NicoleB, Faith

Discription: These CD's put together make a sine function, or if you look at it the other way it would be -sin(x).

Originators: Paul G. and Kristen H.

Photo Description: These are a number of baskets at the front of the Spryfield Superstore. They look much like a sine function, represented by the function y=sin(x).

Originators: Kev B. and Erica

Photo Description: kev.b and ericas fine technology looks like a reflected sine graph

Originator: Victor

Photo Description: The Sobeys' building sign logo located on herring cove road shows a cosine function.

Originators: Ben and Matt

Description: The random arrangement of golf balls represents a sine function with a horizontal translation of 180 degrees.

Originators: Ben and Matt

Photo Description: The linking ropes that border the MacDonald bridge resemble a cosine function with a vertical translation of 1. Although this photo was taken ‘back in Mr. Lee’s day’ the bridge still looks the same today.

**A Note from Mr. Lee about Suspension Bridges:** A free hanging rope or chain follows a curve that is called a catenary. The equation for a catenary is pretty cool and we'll look at it when we get to chapter 3.7 in the textbook ("Modeling with Exponential and Logarithmic Functions"). It turns out however that the cables of a suspension bridge, with the added weight of the deck, form a parabola. The absolute value of a cosine function models the cables approximately but a parabola would give a better fit.