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:
- 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’.
- Remember the acronym ‘SOHCAHTOA’, which stands for:
- Sine = Opposite/Hypotenuse
- Cosine = Adjacent/Hypotenuse
- Tangent = Opposite/Adjacent
- To remember the reciprocals of these trigonometric functions, remember the acronym ‘CAHSHOA’, which stands for:
- Cosecant = Hypotenuse/Opposite
- Secant = Hypotenuse/Adjacent
- Cotangent = Adjacent/Opposite
- To remember the Pythagorean identity, remember the formula:
- sin²θ + cos²θ = 1
- You can also remember it as ‘SohCahToa squared equals one.’
- 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..
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/tanx= cot x
Now, coming to other formulas, you first need to remember the most basic formula of trigonometry:
now, divide(1) by cos²x,
and also, divide (1) by sin²x
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):
- write down 0,30,45,60,90 in a single line (horizontally)
- just below it write 0,1,2,3,4 below these values in the same way
- divide these values (0,1,2,3,4) by 4.
- now take square root of these values
- you will get the values of sin
- now reverse the order for cos
- 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..
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
putting in cos 2x,
cos 2x= cos²x-1+cos²x
cos 2x= 2 cos²x-1
also, cos²x=1- sin²x [from (1)]
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!