# Trigonometry

Do you like studying angles and triangles? Then you’ll love learning trigonometry! Trigonometry is a branch of math that looks at the relationships between side lengths of triangles and their corresponding angles. You’ll be able to use your knowledge of geometry and algebra to derive and employ the trigonometric identities. Trigonometry is essential to the understanding of precalculus.

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## Acute Angles and Right Triangles

This lesson reviews the specific types of triangles as well as fundamental trigonometric identities like sine, cosine and tangent. The ratios of those identities help solve for missing side lengths of triangles and the Pythagorean theorem cannot be used.

## Complex Numbers

Complex numbers are written in the form x+yi, where the y-axis represents the imaginary axis. In polar coordinate form, “x+yi” is written as r(cosθ + i sinθ) where r is the distance from the origin.

## Deriving Trigonometric Identities with Euler’s Formula

This lesson investigates how different trigonometric identities are derived. Read on to learn how to use Euler’s Formula is used to find some important trigonometric identities!

## Half Angle and Double Angle Formulas

This lesson is all about the special relationship between trigonometric functions (like sin, cos, and tan) and their doubles or halves. These formulas are important to know, because they can simplify a much harder equation.

## Inverse Trigonometric Functions

An inverse trig function allows you to input a number and get an angle measure as an output. Typically, you’ll be working in radians when you use inverse trig functions. These functions are read as “arc” + “name of function;” for example, “the arcsine of x,” or sin^{-1}(x).

## Law of Sines

The Law of Sines describes a proportion that can be used to solve for unknown sides and angles in a triangle. Basically, the proportion states that a side length of a triangle, a, directly corresponds to the sine of its opposite angle, A.

## Logarithmic Functions

This lesson breaks down tricky logarithmic functions into their basic components: the base (b), the fixed input value (y), and the output of the function, x.The logarithm is therefore written as b^{x} = y. This lesson also goes over Product Identity, Quotient Identity, Power Identity, and changing bases.

## Converting Between Polar and Rectangular Coordinates

Both polar and rectangular coordinates refer to a point on a chart or graph. Often times, the Pythagorean theorem is used to find the corresponding coordinates. Read this lesson for quick conversion tips!

## Pythagorean Identity

Did you know the Pythagorean theorem, a^{2} + b^{2} = c^{2}, is closely related to the trigonometric identity sin(θ)^{2} + cos(θ)^{2} = 1? Read this lesson to learn how to apply the Pythagorean Identity.

## Converting Between Radians and Degrees

Converting radians to degrees (and vice versa!) is simply another method of unit conversion. To convert, one must understand the relationship between radians and degrees, which is basically π = 180°. Read the entire lesson to discover how to perform this conversion flawlessly!

## Reciprocal Identities

This lesson describes what to do when you see the reciprocal of a function – for example, how do you evaluate ^{1}/_{cos(x)}? Read this lesson to find out!

## Trigonometric Exponential Functions

An exponential function looks like this: f(x) = ab^{x}. This lesson goes over the difference between exponential growth and exponential decay, as well as other ways to look at exponential functions.

## The Unit Circle

The unit circle is one of the most fundamental concepts in math. Here, you’ll be able to revisit the four quadrants as well as static angle measurements (both in radiants and degrees) that are found in each of the quadrants.

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