# Trigonometric Functions Worksheets

In this section of our site, we explore the interactions and uses of trigonometric functions. These are functions that are all related to right-triangles. If you have a right triangle and can determine the measures of two sides, you can use these functions to figure out the measures of all the internal angles within it. You could also use the Pythagorean Theorem to determine the measure of the missing side. They also help you determine angle measures in either degrees or radians. Students can use this collection of worksheets and lessons to learn how to approach and use trigonometric functions.

### Aligned Standard: HSF-TF.A.2

- Cos to Sin Step-by-Step Lesson- A lot of theory goes into understanding and explaining this one.
- Guided Lesson - More transformations from: Tan to Cosec, Sin to Tan, and Cos to Cot.
- Guided Lesson Explanation - Looking back, I could have saved a bit of paper here by condensing the theory into one. This is more complete though.
- Practice Worksheet - If there is such a thing, this is a drill and skill paper on this topic. Instead of the mad minute; consider it a Hurried Hour.
- Matching Worksheet - Most students will jump to the calculator for these. I wrote them as fractions to minimize the help calculators can give you.

- Answer Keys - These are for all the unlocked materials above.
- Homework Sheet - These are setup nicely so that you relate all of the functions together with a known right triangle.
- Independent Practice Worksheet - Determine the value of the missing side in each of these right triangles and then find the value of missing angle measures.
- Quiz 1 - For each right-angled triangle find all the missing measures.
- Quiz 2 - You are given a reference angle and then asked to see how it matches up with another trigonometric function.

### What are Trigonometric Functions?

In math, Trigonometric Functions are also called circular, goniometric, and angle functions. These are real functions, and all are related to the right-angled triangle. These functions are mainly used in geometry especially for navigation, geodesy, and celestial mechanics purposes in the professional world. There are six trigonometric functions in total. All six functions are derived using a right-angled triangle. There are three sides in a right-angled triangle relative to the internal angles of interest: Hypotenuse, opposite (perpendicular) and adjacent side (base). Here are the six trigonometric functions found in math. In order of the Name of Function-Abbreviation-Ratio; they can be stated as:

**Sine A** - Sin A - OPP / HYP, **Cosine A** - Cos A - ADJ / HYP

**Tangent A** - Tan A - OPP / ADJ, **Cosecant A** - Csc A - HYP / OPP

**Secant A - Sec A** - HYP / ADJ, **Cotangent A** - Cot A - ADJ / OPP

It is important to note that there are only three basic trigonometric functions as cosec is the inverse of sine, sec is the inverse of cos, and cotangent is the inverse function of a tangent.

### How Are They Useful in Real Life?

In just about any situation where you are certain that a right-triangle is present, you can easily determine many missing measures that are not measurable. This is absolutely critical in many situations when you are surveying areas that you can not get any equipment to measure anything. A recent use that I read about this week was how cave explorers’ transverse an unexplored or charted cave. They map out the density of the cave triangularly to locate possible opens and ways to pass through it easier. Many mineral and natural resource companies use this type of math to determine the size of natural resource deposits under the Earth’s surface. Just about all aspect of architecture involve this principle to provide the home or building owners with perfectly straight walls.