1 / 10

Trigonometry Formulas

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

28144
Download Presentation

Trigonometry Formulas

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Know All Trigonometry Formulas Formula of Trigonometry: Trigonometry is a well acknowledged name in the geometric domain of mathematics, which is in relevance in this domain since ages and is also practically applied across the number of occasions. Formula of Trigonometry: Trigonometry is a well acknowledged name in the geometric domain of mathematics, which is in relevance in this domain since ages and is also practically applied across the number of occasions.

  2. In simple language trigonometry can be defined as that branch of algebra, which is concerned with the triangle. In this branch we basically study the relationship between angles and side length of a given triangle. With this detailed study of triangle, several types of equations are formed, which are consequently solved to simplify the relationship between the side and angle lengths of such triangle. Trigonometry is considered as one of the oldest components of Algebra, which has been existing around since 3rd century. There are the practical usages of trigonometry in several contexts such as in the domain of astronomy,surveying, optics or in periodic functions.

  3. Formulas of Trigonometry Well, whether it is algebra or geometry both of these mathematics branches are based on scientific calculations of equations and we have to learn the different formulas in order to have its easy calculation. As we know that in Trigonometry we basically measure the different sides of a triangle, by which several equations are formed. Further the formulas of Trigonometry are drafted in accordance to the various ratios used in the domain, such as sine, tangent, cosine etc. So, basically there are the numbers of the formulas which are generally used in Trigonometry to measure the sides of the triangle.

  4. Here below we are mentioning the list of different types of formulas of Trigonometry. 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

  5. The Reciprocal Identities are given as: cosec θ = 1/sin θ sec θ = 1/cos θ cot θ = 1/tan θ sin θ = 1/cosec θ cos θ = 1/sec θ tan θ = 1/cot θ

  6. Periodicity Identities (in Radians) These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called co-function identities. sin (π/2 – A) = cos A & cos (π/2 – A) = sin A sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A sin (π – A) = sin A & cos (π – A) = – cos A sin (π + A) = – sin A & cos (π + A) = – cos A sin (2π – A) = – sin A & cos (2π – A) = cos A sin (2π + A) = sin A & cos (2π + A) = cos A

  7. Co-function Identities (in Degrees) The co-function or periodic identities can also be represented in degrees as: sin(90°−x) = cos x cos(90°−x) = sin x tan(90°−x) = cot x cot(90°−x) = tan x sec(90°−x) = csc x csc(90°−x) = sec x Sum & Difference Identities sin(x+y) = sin(x)cos(y)+cos(x)sin(y) cos(x+y) = cos(x)cos(y)–sin(x)sin(y) tan(x+y) = (tan x + tan y)/ (1−tan x •tan y) sin(x–y) = sin(x)cos(y)–cos(x)sin(y) cos(x–y) = cos(x)cos(y) + sin(x)sin(y) tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)

  8. Double Angle Identities sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)] cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)] cos(2x) = 2cos2(x)−1 = 1–2sin2(x) tan(2x) = [2tan(x)]/ [1−tan2(x)] sec (2x) = sec2 x/(2-sec2 x) csc (2x) = (sec x. csc x)/2 Triple Angle Identities Sin 3x = 3sin x – 4sin3x Cos 3x = 4cos3x-3cos x Tan 3x = [3tanx-tan3x]/[1-3tan2x]

  9. Half Angle Identities sinx2=±1−cosx2 cosx2=±1+cosx2 tan(x2)=1−cos(x)1+cos(x) Also,tan(x2)=1−cos(x)1+cos(x)=(1−cos(x))(1−cos(x))(1+cos(x))(1−cos(x)=(1−cos(x))21−cos2(x)=(1−cos(x))2sin2(x)=1−cos(x)sin(x) So, Product identities sinx⋅cosy=sin(x+y)+sin(x−y)2 cosx⋅cosy=cos(x+y)+cos(x−y)2 sinx⋅siny=cos(x−y)−cos(x+y)2 Sum to Product Identities sinx+siny=2sinx+y2cosx−y2 sinx−siny=2cosx+y2sinx−y2 cosx+cosy=2cosx+y2cosx−y2 cosx−cosy=−2sinx+y2sinx−y2

  10. Inverse Trigonometry Formulas sin-1 (–x) = – sin-1 x cos-1 (–x) = π – cos-1 x tan-1 (–x) = – tan-1 x cosec-1 (–x) = – cosec-1 x sec-1 (–x) = π – sec-1 x cot-1 (–x) = π – cot-1 x Know More AboutyTrigonometry Formulas

More Related