Trigonometric Ratios
Points to remember:
1. Usually, student got confused between perpendicular and base. Always remember that out of three sides, perpendicular is that side which is opposite to the given angle.
In following figure, perpendicular (P) is the side which is opposite to the purple shaded angle(given angle)
2. Side opposite to the right angle(shaded red) is hypotenuse (H).
3. Remaining side is known as base (B).
Now, you must be knowing that all the trigonometric ratios can be derived from these sides. Let us see how.
Sin `theta` = `P/H` Cosec `theta` = `H/P`
Cos `theta` = `B/H` Sec `theta` = `H/B`
Tan `theta` = `P/B` Cot `theta` = `B/P`
Learning all these formulae is somewhat difficult because trigonometry is full of formulas. Let me tell you the very easy method to learn the above formulas.
Following is the basic pattern which you should learn by heart. The easy way to remember this is the way our teachers teach us in schools. I am sure that is the best way to remember this. You can never forget this trick:
(Some People Have) (Curly Brown Hair) (Through Proper Brushing)
Learn the above line and write 33 words vertically like:
Some Curly Through
People Brown Proper
Have Hair Brushing
i.e.
S C T
P B P
H H B
Sin

Cos

Tan

P

B

P

H

H

B

Cosec

Sec

Cot

Basic Formula
 Cosec `theta` = 1/ (Sin `theta`)
 Sec `theta` = 1/ (Cos `theta`)
 Cot `theta` = 1/(tan `theta`)
 Tan `theta` = (Sin `theta`)/(Cos `theta`)
 `Sin^2 theta + Cos^2 theta = 1`
 `1+ tan^2 theta = sec^2 theta`
 `1+ cot^2 theta = cosec^2 theta`
Trigonometric Ratios of Standard Angles
`theta`

0°

30°

45°

60°

90°

Sin `theta`

0

1/2

1/`sqrt2`

`sqrt3`/2

1

Cos `theta`

1

`sqrt3`/2

1/`sqrt2`

1/2

0

Tan `theta`

0

1/`sqrt3`

1

`sqrt3`

Not Defined

Cot `theta`

Not Defined

`sqrt3`

1

1/`sqrt3`

0

Cosec `theta`

1

2/`sqrt3`

`sqrt2`

2

Not Defined

Sec `theta`

Not Defined

2

`sqrt2`

2/`sqrt2`

1

 Write numbers from 0 to 4
 Divide the numbers with 4
 Take the square root of all
1 `to` `1/4` `to` `1/4` `1/2`
2 `to` `2/4` `to` `1/2` Taking Square root `to` `1/sqrt2`
3 `to` `3/4` `to` `3/4` `sqrt3/2`
4 `to` `4/4` `to` `1` 1
See. how simple. You just need to divide 4 to numbers 0 to 4, then take square root.
Row2 = It is just the reverse of Sin values. (See table)
Row3 = Value of tan `theta` is derived by using (Sin `theta`)/(cos `theta`)
Row4 = Use Cot `theta` = 1/ tan `theta`
Row5 = Use Sec `theta` = 1/ cos `theta`
Row6 = Use Cosec `theta` = 1/sin `theta`
Examples with Solution
I hope you understand this topic till now, I will soon update the rest of the topic.
Your valuable feedback will be appreciated.
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