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## Trigonometry

### Course: Trigonometry>Unit 2

Lesson 1: Unit circle introduction

# Trigonometric functions: FAQ

## Where are trigonometric functions used in the real world?

Trigonometric functions are used as models in a wide variety of fields, including engineering, physics, astronomy, and navigation. For example, engineers might use trigonometric functions to describe vibrations or waves, while astronomers might use them to model the orbits of planets.

## What is the unit circle?

The unit circle is a circle with a radius of $1$ centered at the origin. We can use the unit circle to help define the trigonometric functions and visualize their values.
Practice with our Unit circle exercise.

## What are radians and why do we use them in trigonometry?

Radians are a unit of measurement for angles.
One radian is the angle measure that we turn to travel one radius length around the circumference of a circle.
We often use radians in trigonometry because they make working with trigonometric functions easier.
Practice with our Radians & degrees exercise.

## What is the Pythagorean identity?

The Pythagorean identity is an equation that connects sine and cosine. It states that ${\mathrm{sin}}^{2}\left(x\right)+{\mathrm{cos}}^{2}\left(x\right)=1$ for any angle measure $x$.

## What do the graphs of sin(x), cos(x), and tan(x) look like?

The graphs of sin(x) and cos(x) are both sinusoidal, meaning they have a wavy shape that repeats periodically. Tan(x) also repeats periodically, but its graph has discontinuities (places where the function is not defined) and vertical asymptotes.

## What are amplitude, midline, and period?

Amplitude, midline, and period are all terms we use to describe sinusoidal graphs. Amplitude is the height of the wave from the midline, midline is the horizontal line around which the wave oscillates, and period is the length of one complete cycle.

## How do we transform sinusoidal graphs?

We can change the amplitude, midline, and period of a sinusoidal graph by modifying the equation of the function. For example, if we multiply the function by a constant, we change the amplitude. If we add or subtract a constant, we change the midline. And if we multiply the input by a constant, we change the period.

## What's the difference between tau and pi?

Both tau ($\tau$) and pi ($\pi$) are constants related to circles. Tau is equal to two times pi, or roughly $6.28$. Some mathematicians argue that using tau instead of pi makes certain equations and formulas simpler.