Question

What are trigonometric ratios ,explain about all of them

Answer 1

Let ABC be a right-angled triangle with the right angle at C.
The side AB opposite the right angle is called the hypotenuse. This is always the longest side.

Referring to angle A, the opposite side is BC, and the remaining side AC is the adjacent side.
The ratios sine, cosine and tangent are defined as ratios of the three sides.

The mnemonic SOH CAH TOA tells you that:
sin(A) is opposite over hypotenuse (BC/AB);
cos(A) is adjacent over hypotenuse (AC/AB);
tan(A) is opposite over adjacent (BC/ AC).

The ratios for angle B are obtained in the same way, but because AC is the side opposite angle B, that means the adjacent side is BC.
sin(B) is opposite over hypotenuse (AC/AB);
cos(B) is adjacent over hypotenuse (BC/AB);
tan(B) is opposite over adjacent (AC/ BC).

If you know AC and angle B, for example, and want to find AC, then think 'What equation can I write down to give AC?'
AC is opposite B, and you want AB which is the hypotenuse. The ratio is therefore sine. From the definition above:
AC / AB = sin(B).
Take reciprocals of each side to get AB:
AB / AC = 1 / sin(B)
Multiply by AC:
AB = AC / sin(B).

Answer 2

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1. Sine A = BC / AC  

2. Cosine A = AB / AC  

3. Tangent A = BC / AB  

4. Cosecant A = AC / BC  

5. Secant A = AC / AB  

6. Cotangent A = AB / BC  

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1. sin A is written for sine A.  

2. cos A is written for cosine A.  

3. tan A is written for tangent A.  

4. cosec A is written for cosecant A.  

5. sec A is written for secant A.  

6. cot A is written for cotangent A.  

Short way to learn above ratios :  

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