## Graphing Trig Functions Worksheets

#### Aligned To Common Core Standard:

**High School Geometry** - HSG-C.A.2

What are Tangent, Cotangent, Secant, and Cosecant?
Trigonometry is defined as that branch of mathematics that determines relations of angles and sides of a triangle. This branch of mathematics has a few trigonometric ratios that help us in finding the relations between angles and sides of a triangle.
Typically, a triangle is defined with three sides; adjacent, perpendicular and hypotenuse. Using these three sides, we can define the following trigonometric ratios as:
**TANGENT** - Tangent ratio defines the relationship between the perpendicular or opposite side to the adjacent side of a particular angle of the right-angled triangle.
tangent < Θ = opposite/adjacent or tangent < Θ = sinΘ / cosΘ | Note that hypotenuse never changes. It always stays that side opposite to the right angle. However, the opposite and adjacent sides change according to the chosen angle.
**COTANGENT** - Cotangent or cot is the reciprocal function of a tangent function. It is used in the same way as the other trigonometric ratios. Depending on the chosen angle, the opposite and adjacent change.
cotangent < Θ = adjacent/opposite or cotangent < Θ = cosΘ/sinΘ
**COSECANT** - Cosecant is another reciprocal trigonometric ration. It is the reciprocal function of sine. Since sine is defined as the opposite/hypotenuse, cosecant will be defined as hypotenuse/opposite. cosecant < Θ = hypotenuse/opposite.
**SECANT** - Like cosecant, secant is also the reciprocal function of one of the basic trigonometric function. Secant is defined as the reciprocal function of cosine. Since cosine is defined as adjacent/hypotenuse, secant will be defined as hypotenuse/adjacent. secant <Θ = hypotenuse/adjacent
These worksheets and lessons help students learn how to interpret the graph of various trig. functions.

### Printable Worksheets And Lessons

- What's the Graph Step-by-Step Lesson- This one looks like a heart monitor graph.
- Guided Lesson - Lots of different waves for you to define and verify the equation for.
- Guided Lesson Explanation - Unlike many other sections of the site, I talk you through the general process of solving these problems. That is because you are expected to understand determining equations from two points at this point.
- Practice Worksheet - This really is a typical five pack for the site, but it really is just ten problems.
- Matching Worksheet - I just couldn't get the matching equations to fit on a single line with requiring you to use magnifying glasses.
- Graphs Dealing with Tangent, Cotangent, Secant, Cosecant Five Pack of Worksheets - Sorry for the super long title on this one. It is good for you to know what you are walking into though.
- Chords Secants Tangents in Circles Worksheet Five Pack - This pack walk you through the process and basically asks you where you end as a result.

#### Homework Sheets

When you are looking for the equation it is helpful to have a straight edge handy.

- Homework 1 - Analyze the graph carefully.
- Homework 2 - Determine the points on both the axes.
- Homework 3 - Write the equation from the points.

#### Practice Worksheets

Some of the waves as synchronous and some of them don't seem that way at all.

- Practice 1 - Determine the equation of the graph.
- Practice 2 - There is a repeated pattern here, so we first isolate one part of the pattern.
- Practice 3 - Write the equation from the points.