# What is the Antiderivative of trig functions?

Space and AstronomyThis 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 = sec^{2}x |
sec^{2}x dx = tan x + C |

d dx cotan x = − cosec^{2}x |
cosec^{2}x 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 |

sin^{2}x |
x/2 – sin(2x)/4 + c = (x – sinx ∙ cosx)/2 + c |

cos^{2}x |
x/2 + sin(2x)/4 + c = (x + sinx ∙ cosx)/2 + c |

tanx = sec^{2}x |
-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 sin^{2} 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 = ∫ (sec^{2}x + 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 |

sec^{2} x dx = tan x + C Proof |
csc^{2} 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:**

- Find the vertical asymptotes so you can find the domain. …
- Find the values for the range. …
- Determine the x-intercepts. …
- 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.*

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