Posted on April 27, 2022 (Updated on July 9, 2025)

What is the Antiderivative of trig functions?

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This Section: 4. Integrals of Trigonometric Functions

Derivative Rule Antiderivative Rule
d dx sin x = cos x cos x dx = sin x + C
d dx cos x = − sin x sin x dx = − cos x + C
d dx tan x = sec2x sec2x dx = tan x + C
d dx cotan x = − cosec2x cosec2x dx = − cotan x + C

What is the antiderivative of Trig?

Video quote: And we call this function the antiderivative of f of X equals cosine. X. So the reverse of differentiating is anti-differentiating and the result is called the antiderivative.

What are the integrals of trigonometric functions?

Integrals of Trigonometric Functions

Function Integral
cosx sinx + c
sin2x x/2 – sin(2x)/4 + c = (x – sinx ∙ cosx)/2 + c
cos2x x/2 + sin(2x)/4 + c = (x + sinx ∙ cosx)/2 + c
tanx = sec2x -ln|cosx| + c

Is sin the only antiderivative of Cos?

What is the antiderivative of cosx. Again, people memorize that the antiderivative of cosx is sinx.

What is the general antiderivative of a sine function?

These equations can be integrated to get two equally common antiderivative statements: sin(x)+C=∫cos(x)dx. cos(x)+C=∫−sin(x)dx.

What’s the antiderivative of cosine?

Thus we sometimes say that the antiderivative of a function is a function plus an arbitrary constant. Thus the antiderivative of cos ⁡ x \cos x cosx is ( sin ⁡ x ) + c (\sin x) + c (sinx)+c. The more common name for the antiderivative is the indefinite integral.

What is the antiderivative of sin2x?

Answer: The antiderivative of sin2 x is x/ 2 – (sinx cosx) / 2.

What is the antiderivative of Cos 2x?

1/2 sin2x + c

The integral, or antiderivative, of cos2x is 1/2 sin2x + c.

What is the antiderivative of cos3x?

The antiderivative of cos 3x is ∫cos 3x dx = (1/3) sin 3x + C, where C is the constant of integration.

What is the antiderivative of CSC 2?

The antiderivative of csc2x is −cotx+C .

What is antiderivative of csc?

Calculus Examples



The integral of csc(x) with respect to x is ln(|csc(x)−cot(x)|) ln ( | csc ( x ) – cot ( x ) | ) . ln(|csc(x)−cot(x)|)+C. The answer is the antiderivative of the function f(x)=csc(x) f ( x ) = csc ( x ) .

What is the antiderivative of Secx?

The antiderivative of sec x is mathematically writen as ∫ sec x dx. Multiply and divide sec x by (sec x + tan x), we get, ∫ sec x dx = ∫ sec x · (sec x + tan x) / (sec x + tan x) dx = ∫ (sec2x + sec x tan x) / (sec x + tan x) dx.

What is the antiderivative of csc cot?

Math2.org Math Tables: Table of Integrals

cos x dx = sin x + C Proof csc x cot x dx = – csc x + C Proof
sin x dx = -cos x + C Proof sec x tan x dx = sec x + C Proof
sec2 x dx = tan x + C Proof csc2 x dx = – cot x + C Proof


What is csc equal to?

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

Where is cot on ti84?

Video quote: But there are no cosecant cotangent or secant functions. So we can sort of get around this by using fractions.

How do you write cosecant?

Cosecant is one of the main six trigonometric functions and is abbreviated as csc x or cosec x, where x is the angle. In a right-angled triangle, cosecant is equal to the ratio of the hypotenuse and perpendicular. Since it is the reciprocal of sine, we write it as csc x = 1 / sin x.

How do you graph Cotan functions?

To sketch the full parent graph of cotangent, follow these steps:

  1. Find the vertical asymptotes so you can find the domain. …
  2. Find the values for the range. …
  3. Determine the x-intercepts. …
  4. Evaluate what happens to the graph between the x-intercepts and the asymptotes.


How do you graph tan and cot trig functions?

Video quote: But you want to draw your curves going the other way so tangent would start off at this write asymptote. And then start hugging. Towards this way a lot like X cubed cotangent. Works the other way.

What are trigonometric graphs?

To sketch the trigonometry graphs of the functions – Sine, Cosine and Tangent, we need to know the period, phase, amplitude, maximum and minimum turning points. These graphs are used in many areas of engineering and science.

How do you find the equation of a Secantant graph?

Video quote: The distance from the midline to a maximum this distance here is 2 units and therefore the amplitude is 2. But is also the distance from the midline to a minimum. Which we see here.

How do you write an equation for a trig graph?

Video quote: And you multiply both sides by the absolute value of B. And then divide by the period it tells you that the absolute value of B is equal to two pi divided.

How do you find an equation of the secant and cosecant functions if the graph of the function is provided?

Video quote: Minus negative one simplifies to x plus one. And then we have minus one which means for the original graph that was given in black. We could also find the function in terms of cosecant.

How do you write secant?

(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. In a formula, it is abbreviated to just ‘sec’.

How do you solve cosecant?

Video quote: You need to understand what is my angle is my angle in radians or is it in degrees a. Very easy method is obviously if you have that degree.

How do you find sine?

Video quote: So sine would simply be 5 thirteenth's.