# What are the 9 trig identities?

## What are the 9 trig identities?

Trigonometric Identities List

• Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
• Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
• Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

What is the reciprocal of sin A?

The cosecant is the reciprocal of the trigonometric function sine. It can be calculated by dividing the hypotenuse by the side opposite a given angle in a right triangle.

### What jobs use trigonometry?

Trigonometry is used by engineers, medical services technicians, mathematicians, data entry specialists, loggers, statisticians, actuaries, drafters, chemists, economists, physicists, registered nurses, building inspectors, boilermakers, machinists and millwrights.

What is tan inverse equal to?

Basic idea: To find tan-1 1, we ask “what angle has tangent equal to 1?” The answer is 45°. As a result we say that tan-1 1 = 45°. In radians this is tan-1 1 = π/4….index: subject areas.

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## What is sin 3x formula?

\sin 3x =4\sin x\sin(60^{\circ}-x)\sin(60^{\circ}+x). We first remind of another useful trigonometric identity: \displaystyle\sin\alpha + \sin\beta +\sin\gamma -\sin(\alpha +\beta +\gamma)=4\sin\frac{\alpha +\beta}{2}\sin\frac{\beta +\gamma}{2}\sin\frac{\gamma +\alpha}{2}.

What is the basis of trigonometry?

There are three basic functions in trigonometry, each of which is one side of a right-angled triangle divided by another. You may find it helpful to remember Sine, Cosine and Tangent as SOH CAH TOA.

### Who invented trigonometry?

Trigonometry in the modern sense began with the Greeks. Hipparchus (c. 190–120 bce) was the first to construct a table of values for a trigonometric function.

What is the COS inverse of?

The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number….arccos.

cos30 = 0.866 Means: The cosine of 30 degrees is 0.866
arccos 0.866 = 30 Means: The angle whose cosine is 0.866 is 30 degrees.

## What are the 6 reciprocal identities?

Terms in this set (6)

• sin. 1/csc.
• cos. 1/sec.
• tan. 1/cot.
• cot. 1/tan.
• sec. 1/cos.
• csc. 1/sin.

What is COS 1 equal to?

As you can see below, the cos-1 (1) is 270° or, in radian measure, 3Π/2 . ‘-1’ represents the minimum value of the cosine function ever gets and happens at Π and then again at 3Π ,at 5Π etc..

### Who is father of trigonometry?

Hipparchus of Nicaea

How do you convert trigonometric functions?

Transformations of Trigonometric Functions

1. Vertical and Horizontal Shifts. Suppose c > 0. To obtain the graph of. y = f(x) + c: Shift the graph of y = f(x) up by c units.
2. Vertical and Horizontal Stretches/Compressions. Suppose c > 1. To obtain the graph of.
3. Reflections. To obtain the graph of. y = -f(x): reflect the graph of y = f(x) about the x-axis; and.

## Is Arctan inverse tan?

The arctan function is the inverse of the tangent function. It returns the angle whose tangent is a given number….arctan.

tan 30 = 0.577 Means: The tangent of 30 degrees is 0.577
arctan 0.577 = 30 Means: The angle whose tangent is 0.577 is 30 degrees.

What are the formulas for trigonometry?

Basic Trigonometric Function Formulas

• sin θ = Opposite Side/Hypotenuse.
• cos θ = Adjacent Side/Hypotenuse.
• tan θ = Opposite Side/Adjacent Side.
• sec θ = Hypotenuse/Adjacent Side.
• cosec θ = Hypotenuse/Opposite Side.
• cot θ = Adjacent Side/Opposite Side.

### What is transformation formula?

1. Transformation of an equation into another equation whose roots are. reciprocals of the roots of a given equation we replace x→x1​ 2. Transformation of an equation into another equation whose roots are negative of the roots of a given equation we replace x→−x.

Is sin even or odd?

Sine is an odd function, and cosine is an even function. You may not have come across these adjectives “odd” and “even” when applied to functions, but it’s important to know them. A function f is said to be an odd function if for any number x, f(–x) = –f(x).

## What is transformation in trigonometry?

The graphs of the six basic trigonometric functions can be transformed by adjusting their amplitude, period, phase shift, and vertical shift. Amplitude. The amplitude of a sinusoidal trig function (sine or cosine) is it’s ‘height,’ the distance from the average value of the curve to its maximum (or minimum) value.

Why Sine is called sine?

The word “sine” (Latin “sinus”) comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.

### What is the formula of tan inverse?

To solve the different types of inverse trigonometric functions, inverse trigonometry formulas are derived from some basic properties of trigonometry….Inverse Trigonometric Formulas List.

S.No Inverse Trigonometric Formulas
29 tan-1(tan θ) = θ, -π/2 < θ < π/2
30 cosec-1(cosec θ) = θ, – π/2 ≤ θ < 0 or 0 < θ ≤ π/2

How do you prove identity?

For instance, sin(x) = 1/csc(x) is an identity. To “prove” an identity, you have to use logical steps to show that one side of the equation can be transformed into the other side of the equation. You do not plug values into the identity to “prove” anything.

## What is Arctan formula?

Arctan definition The arctangent of x is defined as the inverse tangent function of x when x is real (x∈ℝ). When the tangent of y is equal to x: tan y = x. Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y: arctan x= tan-1 x = y.

How is Atan calculated?

Tan and Atan are useful for converting between degrees of slope and percentage of slope or “rise over run.” Usually a “25% slope” means that b/a = 0.25 in the figure above. The corresponding degrees of slope would be Atan(b/a) converted into degrees, or Atan(b/a) *180/Pi. If b/a = 25%, then X = 14 degrees.

### What are the 3 trigonometric identities?

The three main functions in trigonometry are Sine, Cosine and Tangent….Sine, Cosine and Tangent.

Sine Function: sin(θ) = Opposite / Hypotenuse
Tangent Function: tan(θ) = Opposite / Adjacent

What are the 2 quotient identities?

In trigonometry, quotient identities refer to trig identities that are divided by each other. There are two quotient identities that are crucial for solving problems dealing with trigs, those being for tangent and cotangent. Cotangent, if you’re unfamiliar with it, is the inverse or reciprocal identity of tangent.

## Who invented inverse trigonometry?

Daniel Bernoulli

What is the reciprocal of Tanθ?

The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine function is cosecant, csc(theta)=1/sin(theta). The reciprocal tangent function is cotangent, expressed two ways: cot(theta)=1/tan(theta) or cot(theta)=cos(theta)/sin(theta).

### Is SEC the inverse of cos?

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

What’s a quotient identity?

Definition. Quotient Identity. The quotient identity is an identity relating the tangent of an angle to the sine of the angle divided by the cosine of the angle.