These functions are called circular functions because **radian measures of angles are determined by the lengths of arcs of circles**. In particular, trigonometric functions defined using the unit circle lead directly to these circular functions.

Trigonometric identities are **equations involving the trigonometric functions that are true for every value of the variables involved**. Some of the most commonly used trigonometric identities are derived from the Pythagorean Theorem , like the following: sin2(x)+cos2(x)=1. 1+tan2(x)=sec2(x)

**Trigonometry**

- The Pythagorean Theorem.
- Special Right Triangles.
- Basic Trigonometric Functions.
- Solving Right Triangles.
- Measuring Rotation.
- Applying Trig Functions to Angles of Rotation.
- Trigonometric Functions of Any Angle.
- Relating Trigonometric Functions.

These are the two most basic trigonometric functions from which other four basic trigonometric functions tanθ, secθ, cosec θ and cot θ are derived, **tanθ=heightbase=hb=sinθcosθ**, it is the ratio of the two primary functions. secθ=hypotenusebase=lb=1cosθ, it is just the inverse of cosθ.

In trigonometry, there are six trigonometric ratios, namely, **sine, cosine, tangent, secant, cosecant, and cotangent**. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

**Terms in this set (11)**

- sinx. 1/cscx.
- cosx. 1/secx.
- tanx. 1/cotx.
- cscx. 1/sinx.
- secx. 1/cosx.
- cotx. 1/tanx.
- tanx. sinx/cosx.
- cotx. cosx/sinx.

The three trig ratios in question are **sine (sin), cosine (cos) and tangent (tan)**.

Trigonometry has 6 basic trigonometric functions, they are **sine, cosine, tangent, cosecant, secant, and cotangent**.

The following are the identities of inverse trigonometric functions: sin^{-}^{1} (sin x) = x provided –π/2 ≤ x ≤ π/2. cos^{-}^{1} (cos x) = x provided 0 ≤ x ≤ π tan^{-}^{1} (tan x) = x provided –π/2 < x < π/2.

1 : a function (such as the sine, cosine, tangent, cotangent, secant, or cosecant) of an arc or angle most simply expressed in terms of the ratios of pairs of sides of a right-angled triangle. — called also circular function. 2 : the inverse (such as the arcsine, arccosine, or arctangent) of a trigonometric function.

Brahmagupta

Hipparchus was born in **Nicaea, Bithynia**, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.

There are four types of trigonometry used today, which include **core, plane, spherical and analytic**. Core trigonometry deals with the ratio between the sides of a right triangle and its angles.

mathematician Hipparchus

With that in mind, in order to have an inverse function for trigonometry, we restrict the domain of each function, **so that it is one to one**. A restricted domain gives an inverse function because the graph is one to one and able to pass the horizontal line test.

These functions are called circular functions because **radian measures of angles are determined by the lengths of arcs of circles**. In particular, trigonometric functions defined using the unit circle lead directly to these circular functions.

How do you find the inverse of a function? To find the inverse of a function, **write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y**.

The **two** different types of trigonometry are: Plane Trigonometry. Spherical Trigonometry.

Sin θ / Cos θ. This means that: **Sin θ = Cos θ × Tan θ and**. **Cos θ = Sin θ / Tan θ**.

Introducing Sine, Cosine and Tangent.

Name | Abbreviation | Relationship to sides of the triangle |
---|---|---|

Sine | Sin | Sin (θ) = Opposite/hypotenuse |

Cosine | Cos | Cos (θ) = Adjacent/hypotenuse |

Tangent | Tan | Tan (θ) = Opposite/adjacent |

**Cosine and secant** are our even functions where sine, tangent, cosecant and cotangent are our odd functions.

The inverse trig functions are often called "arc functions", **since given a value of a trig function, they produce the length of arc needed to obtain that value**. For example, the inverse sine function can be written as either sin−1x or as arcsinx.

Dated : 02-Jun-2022

Category : Education