what are all the trigonometric RATIO and IDENTITIES?

Answer 1

all above

Answer 2

Here is something I know.

If ABC is a right angled triangle with C as the right angle(90).

AB is the hypotenus.

Let x be an angle in the triangle , either A, B or C
Then ,
sine x = (side opposite x)/hypotenuse

cosine x = (side adjacent x)/hypotenuse

tangent x = (side opposite x)/(side adjacent x)

Are the Ratios.

For Identities, check the below link.

Peace out.

Answer 3

30 - 60 - 90 Right Triangle

let

3 = adjacent side

4 = opposite side

5 = hypotenuse

sinΘ = opposite / hypotenuse

cosΘ = adjacent / hypotenuse

tanΘ = opposite / adjacent

- - - - - - -

Ratio

sinΘ = 4/5

cosΘ = 3/5

tanΘ = 4/3

- - - - - - - -s-

Answer 4

you need to know the basic trig identities like sin² + cos² is 1 and sin2x = 2sinxcosx and cos2x = cos² - sin²x = 2cos²x -1 = 1 - 2sin ²x there are many others of course, but you just need to spot when to use them, or when to use valid substitutions - like sinx / cosx is tanx.

Answer 5

trignometric ratios are sine, cosine, tangent, cotangent,secant and cosecant.......
in a right angled triangle the side opposite to the angle is known as opposite(opp), the side opp. 2 90 degree is known as hypotenous(hyp), the other side is known as adjacent(adj)...
sin=opp/hyp
cos=adj/hyp
tan=opp/adj
sec=hyp/adj
cosec=hyp/opp
cot=adj/opp
identities are equations which satisfies all sets of angles
some are
(sin)sq+(cos)sq=1
(tan)sq+1=(sec)sq
(cot)sq+1=(cosec)sq
sq=square

Answer 6

sin x=opposite side/hypoteuse
cos x=adjacent side/hypotenuse
tan x= opposite side/adjacentside also ( sinx/cosx)
cot x=1tanx=adjacent side/opposite side (1/tanx)
sec x=reciprocal of cos x=hypotenuse/adjacent side
cosec x=reciprocal of sin x=hypotenuse/opposite side

some identities
sin^2x+cos^2x=1
1+tan^2x=sec^2x
1+cot^2x=csc^2x
sin 2x=2sinxcosx
cos 2x=cos^2x-sin^2x
tan2x=2tanx/1-tan^2x
sin(x+y)=sinxcosy+cosxsiny
sin(x-y)=sinxcosy-cosxsiny
cos(x+y)=cosxcosy-sinxsiny
cos(x-y)=cosxcosy+sinxsiny

IDENTITIES
cos^2x+ sin^2x = 1
then with this you can find out sin^2x, cos^2x by equating.
1+tan^2x=sec^2x.
similarly equate to find out the rest.
cot^2x+1= cosec^2x.

tan(90-x)= cotx
cot(90-x)-tanx
sec(90-x)= cosecx
that's all i know

Answer 7

trigonoetric ratios
sin x=opposite side/hypoteuse
cos x=adjacent side/hypotenuse
tan x= opposite side/adjacentside
cot x=1tanx=adjacent side/opposite side
sec x=reciprocal of cos x=hypotenuse/adjacent side
cosec x=reciprocal of sin x=hypotenuse/opposite side

some identities
sin^2x+cos^2x=1
1+tan^2x=sec^2x
1+cot^2x=csc^2x
sin 2x=2sinxcosx
cos 2x=cos^2x-sin^2x
tan2x=2tanx/1-tan^2x
sin(x+y)=sinxcosy+cosxsiny
sin(x-y)=sinxcosy-cosxsiny
cos(x+y)=cosxcosy-sinxsiny
cos(x-y)=cosxcosy+sinxsiny