Master TRICK IN REMEMBERING TRIGONOMETRIC FORMULAS in 5 Minutes A Day

Master TRICK IN REMEMBERING TRIGONOMETRIC FORMULAS in 5 Minutes A Day: Trigonometric formulas can seem overwhelming at first, but with some practice and the right approach, they can be easy to remember. Here’s a simple trick you can use to remember the basic trigonometric formulas:

1. Draw a right-angled triangle and label its sides as follows:
   • The hypotenuse is always opposite the right angle and is labeled ‘h’.
   • The side adjacent to the angle you are interested in is labeled ‘a’.
   • The side opposite to the angle you are interested in is labeled ‘o’.
2. Remember the acronym ‘SOHCAHTOA’, which stands for:
   • Sine = Opposite/Hypotenuse
   • Cosine = Adjacent/Hypotenuse
   • Tangent = Opposite/Adjacent
3. To remember the reciprocals of these trigonometric functions, remember the acronym ‘CAHSHOA’, which stands for:
   • Cosecant = Hypotenuse/Opposite
   • Secant = Hypotenuse/Adjacent
   • Cotangent = Adjacent/Opposite
4. To remember the Pythagorean identity, remember the formula:
   • sin²θ + cos²θ = 1
   • You can also remember it as ‘SohCahToa squared equals one.’
5. To remember the angle sum and difference identities, remember the formulas:
   • sin(α ± β) = sinα cosβ ± cosα sinβ
   • cos(α ± β) = cosα cosβ ∓ sinα sinβ
   • tan(α ± β) = (tanα ± tanβ) / (1 ∓ tanα tanβ)

Yes!! There are many tricks that I have figured out myself (I don’t know about others).. First of all, for basic ratio, if you are an Indian, you will love this sentence (xD) :

Pakistan bhookha pyaasa ,

Hindustan hara bhara.

Take the first initials of words in first line and divide them by corresponding initials of word in second line.

P/h b/h p/b

and the sequence is

sinx cosx tanx

assign these ratios..

sinx= p/h

cosx=b/h

tanx=p/b

where, p= perpendicular ,b= base and h= hypotenuse

[I was taught this sentence in class ten and now still I use this sentence in class XII]

Also, you need to learn

1/sinx = cosec x

1/cosx= secx

1/tanx= cot x

Now, coming to other formulas, you first need to remember the most basic formula of trigonometry:

sin²x+cos²x=1 —(1)

now, divide(1) by cos²x,

tan²x+1=sec²x

and also, divide (1) by sin²x

1+cot²x=cosec²x

Now, for remembering values, you just need to remember valued of sin and you can figure out the rest(I will tell)

Steps to get values of sin(0–90):

1. write down 0,30,45,60,90 in a single line (horizontally)
2. just below it write 0,1,2,3,4 below these values in the same way
3. divide these values (0,1,2,3,4) by 4.
4. now take square root of these values
5. you will get the values of sin
6. now reverse the order for cos
7. divide corresponding value of sin with cos and write them for tan

Generate a table like this and see the values corresponding to angle of sin/cos/tan.

For cosec/sec/cot, divide divide 1 by these values for example cot 45=1/tan45 =1.

Now, there comes some more formulas..

sin(x+y)= sinx.cosy+cosx.siny

sin(x-y)= sinx.cosy-cosx.siny

cos(x+y)= cosx.cosy-sinx.siny

cos(x-y)= cosx.cosy+sinx.siny

now for formula of sin 2x, from sin(x+y),

sin(x+x)= sinx.cosx+ sinx.cosx

sin 2x= 2sinx.cosx

for cos 2x, from cos(x+y)

cos(x+x)= cosx.cosx – sinx.sinx

cos 2x= cos²x-sin²x

but, sin²x+cos²x=1,

so, sin²x=1-cos²x

putting in cos 2x,

cos 2x= cos²x-1+cos²x

cos 2x= 2 cos²x-1

also, cos²x=1- sin²x [from (1)]

cos 2x=1-sin²x-sin²x

cos 2x=1–2sin²x

Well, this way, all formulas are inter-related and you can derive them whenever you need if you know the right trick. This makes trigonometry easier!(There are more formulas which you need to remember also)

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Thanks for reading!