# What are the 6 trigonometric functions and their definitions?

The 6 Trig Ratios. For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Here are the formulas for these six trig ratios: Given a triangle, you should be able to identify all 6 ratios for all the angles (except the right angle).

Keeping this in consideration, what is the rule for Sin Cos Tan?

The functions of sin, cos and tan can be calculated as follows: Sine Function: sin(θ) = Opposite / Hypotenuse. Cosine Function: cos(θ) = Adjacent / Hypotenuse. Tangent Function: tan(θ) = Opposite / Adjacent.

What is sine and cosine?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

What do you call sin cos and tan?

Introduction: In this lesson, three trigonometric ratios (sine, cosine, and tangent) will be defined and applied. These involve ratios of the lengths of the sides in a right triangle. In a right triangle, one angle is 90º and the side across from this angle is called the hypotenuse.

## What is sine cosine and tangent?

Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: “Opposite” is opposite to the angle θ “Adjacent” is adjacent (next to) to the angle θ

## What are the three basic trigonometric ratios?

Remember that the two sides of a right triangle which form the right angle are called the legs , and the third side (opposite the right angle) is called the hypotenuse . There are three basic trigonometric ratios: sine , cosine , and tangent .

## What are the six trigonometric functions and their ratios?

There are six main trigonometric functions:

• Sine (sin)
• Cosine (cos)
• Tangent (tan)
• Secant (sec)
• Cosecant (csc)
• Cotangent (cot)
• ## How do you find the six trigonometric functions?

To evaluate the six trigonometric functions of 225 degrees using the unit circle, follow these steps:

• Draw the picture.
• Fill in the lengths of the legs and the hypotenuse.
• Find the sine of the angle.
• Find the cosine of the angle.
• Find the tangent of the angle.
• Find the cosecant of the angle.
• ## What are the trig functions?

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. The most familiar trigonometric functions are the sine, cosine, and tangent.

## What is the ratio of tangent?

The tangent ratio is a tool used with right triangles that allows one to find the length of the sides of a triangle given the degree of its angles. It can also be used to find the degrees of its angle given the length of two of its sides.

## How do you solve trigonometric ratios?

There are three steps:

• Choose which trig ratio to use. – Choose either sin, cos, or tan by determining which side you know and which side you are looking for.
• Substitute.
• Solve.
• Step 1: Choose which trig ratio to use.
• Step 2: Substitute.
• Step 3: Solve.
• Step 1: Choose the trig ratio to use.
• Step 2: Substitute.
• ## What is the ratio of a cosine?

The hypotenuse in a right triangle is always larger than the adjacent side, so for angles greater than zero but less than 90º the cosine ratio will be less than 1. For angles outside of these limits, the sine ratio can have values from -1 to 1.

## What are the trigonometric identities?

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

## What is the angle of elevation?

The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer’s eye (the line of sight).

## What do you mean by trigonometry?

Trigonometry (from Greek trigōnon, “triangle” and metron, “measure”) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

## What is Sohcahtoa mean?

“SOHCAHTOA” is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent, (1)

## What are the three Pythagorean identities?

The identity is given by the formula: (Note that sin2 θ means (sin θ)2). This relation between sine and cosine is sometimes called the fundamental Pythagorean trigonometric identity. Therefore, this trigonometric identity follows from the Pythagorean theorem.

## What is the opposite of sine?

In addition to sine, cosine, and tangent, there are three other trigonometric functions you need to know for the Math IIC: cosecant, secant, and cotangent. These functions are simply the reciprocals of sine, cosine, and tangent. Cotangent is the reciprocal of tangent.

## What is SEC in trig?

Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. sec x = 1. cos x.

## How many different trigonometric functions are there?

I will present the arguments for 1, 3, 6, and at least 12. The calculator answer: 3. A typical calculator has three trig functions if it has any: sine, cosine, and tangent. The other three that you may see — cosecant, secant, and cotangent — are the reciprocals of sine, cosine, and tangent respectively.

## What is OPP over adj?

All the other trig functions of the first kind can be derived from these two funcions. Futhermore, the sin(x) / cos(x) = (opp/hyp) / (adj/hyp) = opp / adj = tan(x). Therefore, the tangent function is the same as the quotient of the sine and cosine functions (the tangent function is still fairly handy).

## Is the inverse of sin CSC?

Finding the inverse of sine is finding the function “going in the opposite direction” (this is arcsin). Finding the reciprocal of sine is dividing 1 by it (this gives you cosecant). They aren’t the same at all, and it’s unfortunate that the notation confuses people into thinking otherwise.

## What is the COT in trig?

cotangent(q) = adj/opp. The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). It is often simpler to memorize the the trig functions in terms of only sine and cosine: sine(q) = opp/hyp.

## How do you find the sine of an angle?

Step 2 Use SOHCAHTOA to decide which one of Sine, Cosine or Tangent to use in this question. Step 3 For Sine calculate Opposite/Hypotenuse, for Cosine calculate Adjacent/Hypotenuse or for Tangent calculate Opposite/Adjacent. Step 4 Find the angle from your calculator, using one of sin-1, cos-1 or tan.