(Math | Calculus | Derivatives | Table Of)

sin x = cos x Proof | csc x = -csc x cot x Proof |
---|---|

cos x = - sin x Proof | sec x = sec x tan x Proof |

tan x = sec^{2} x Proof | cot x = - csc^{2} x Proof |

Similarly, you may ask, what is the tangent of 0?

So let's take a closer look at the sine and cosines graphs, keeping in mind that

**tan**(θ) = sin(θ)/cos(θ). The**tangent**will be**zero**wherever its numerator (the sine) is**zero**. This happens at**0**, π, 2π, 3π, etc, and at –π, –2π, –3π, etc.How do you find the equation of a tangent line?

1)

**Find**the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to**find**the slope at x. 3) Plug x value into f(x) to**find**the y coordinate of the**tangent**point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to**find**the**equation**for the**tangent line**.1

## What is the derivative of a tangent?

The

**derivative of tan**x is sec2x. However, there may be more to finding**derivatives of tangent**. In the general case,**tan**x is the**tangent**of a function of x, such as**tan**g(x).2

## What is the chain rule for differentiation?

DIFFERENTIATION USING THE

**CHAIN RULE**. The following problems require the use of the**chain rule**. The**chain rule**is a**rule**for differentiating compositions of functions. In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . Most problems are average.3

## What is the Cotangent?

Cosecant, Secant, and

**Cotangent**. 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. Cosecant. Cosecant is the reciprocal of sine.4

## What is implicit differentiation in calculus?

**Implicit differentiation**is nothing more than a special case of the well-known chain rule for derivatives. The majority of

**differentiation**problems in first-year

**calculus**involve functions y written EXPLICITLY as functions of x . For example, if. , then the

**derivative**of y is.

5

## What is the differentiation of sin2x?

To

**differentiate**f(x)=**sin(2x**), simply use the chain rule. Namely, dy/dx= 2*cos(2x). The**derivative of**the sin(x) with respect to x is the cos(x), and the**derivative of**2x with respect to x is simply 2.6

## What is cot to?

The trig function

**cotangent**, written**cot**θ.**cot**θ equals or . For acute angles,**cot**θ can be found by the SOHCAHTOA definition, shown below on the left. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. f(x) =**cot**x is a periodic function with period π.7

## Can you differentiate sin squared?

f(x) = (

**sin**x)**be written as f(u) = u**^{2}can**where u =**^{2}**sin**x. The Chain Rule states that to**differentiate**a composite function**we differentiate**the outer function and multiply by the**derivative**of the inner function.**We can**use the rules cos x =**sin**( /**– x) and**_{2}**sin**x = cos( /**– x) to find the**_{2}**derivative**of cos x.8

## What is CSC?

A Common Service Center (

**CSC**) is an information and communication technology (ICT) access point created under the National e-Governance Project of the Indian government. The project plan includes the creation of a network of over 100,000 CSCs throughout the country.9

## What is the derivative of cos 2?

The derivative of cos(2x) is -2sin(2x). The process of finding this derivative uses the

**chain rule**. We can use integrals to check our work when finding derivatives. If D(x) is the derivative of f(x), then the integral of D(x) is f(x) + C, where C is a constant.10

## Is tangent equal to sine over cosine?

So far in this course, the only trigonometric functions which we have studied are sine and

**cosine**. The**tangent**of x is defined to be its sine divided by its**cosine**:**tan**x =**sin**x**cos**x . The**cotangent**of x is defined to be the**cosine**of x divided by the sine of x: cot x =**cos**x**sin**x .11

## What is the Antideriv of Cos?

Thus we sometimes say that the

**antiderivative**of a function is a function plus an arbitrary constant. Thus the**antiderivative of cos x**is (sin x) + c. The more common name for the**antiderivative**is the indefinite integral.12

## Is SEC the same as 1 cos?

**Secant**, cosecant and cotangent, almost always written as

**sec**, cosec and cot are trigonometric functions like sin,

**cos**and tan. Note,

**sec**x is not the same as

**cos**

^{-}

**x (sometimes written as arccos x). Remember, you cannot divide by zero and so these definitions are only valid when the denominators are not zero.**

^{1}13

## What is the quotient rule?

In calculus, the

**quotient rule**is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let where both and are differentiable and. The**quotient rule**states that the derivative of is.14

## What is the Arctan equal to?

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.15

## What is the equivalent of Secant?

Here are two helpful hints: Each of those definitions has a cofunction on one and only one side of the equation, so you won't be tempted to think that sec A

**equals**1/sin A. And**secant**and cosecant go together just like sine and cosine, so you won't be tempted to think that cot A**equals**1/sin A.16

## What is the meaning of Arccos?

When the cosine of y is equal to x: cos y = x. Then the

**arccosine**of x is equal to the inverse cosine function of x, which is equal to y:**arccos**x = cos^{-}^{1}x = y. (Here cos^{-}^{1}x means the inverse cosine and does not mean cosine to the power of -1).17

## What is the Sinh?

Trigonometry/Cosh,

**Sinh**and Tanh. The functions cosh x,**sinh**x and tanh x have much the same relationship to the rectangular hyperbola y^{2}= x^{2}- 1 as the circular functions do to the circle y^{2}= 1 - x^{2}. They are therefore sometimes called the hyperbolic functions (h for hyperbolic).18

## What is the CSC in trig?

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: sin(q) = opp/hyp.**csc**(q) = 1/sin(q)19

## What is the secant of an angle?

**Secant**(sec) - Trigonometry function. (See also

**Secant**of a circle). In a right triangle, the

**secant**of an angle is the length of the hypotenuse divided by the length of the adjacent side.

20

## What is the CSC in math?

cotangent(q) = adj/opp. Furthermore, the functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (

**csc**), secant (sec), and cotangent (cot).