# Graphing Trig Functions Worksheets Worksheets

These worksheets and lessons help students learn how to interpret the graph of various trig. functions. We use these functions to determine the measures of unknown sides, angles, and distances within geometric systems. When used properly we can completely model geometric situations. We now explore this further by interpreting positioning through the use of expressions and equations.

### Aligned Standard: HSG-C.A.2

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

### Math Skill Quizzes

Always look for the peaks and valleys to help you find the equation.

- Quiz 1 - You will need to diagnose the type of wave you are looking at before you make a move.
- Quiz 2 - Where does this equation bring you?
- Quiz 3 - What is the value of the y-intercept, start there.

### 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. The most common trigonometric ratios are sine, cosine, and tangent, but there are several others that we can use to better understand a system of measures. 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 functions. 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.

We commonly use these trigonometric ratios to solve situations where we have a right triangle involved. These are seen a reciprocal functions.