- Trignometry concepts
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- Trigonometric Ratio’s
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- Trigonometric Ratio’s of Common angles
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- Trigonometric ratio’s of complimentary angles
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- Trigonometric identities

Trigonometry is most simply associated with planar right angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles

In a right angle triangle ABC where B=90° ,

We can define following term for angle A

Base : Side adjacent to angle

Perpendicular: Side Opposite of angle

Hypotenuse: Side opposite to right angle

**We can define the trigonometric ratios for angle A as**

sin A= Perpendicular/Hypotenuse =BC/AC

cosec A= Hypotenuse/Perpendicular =AC/BC

cos A= Base/Hypotenuse =AB/AC

sec A= Hypotenuse/Base=AC/AB

tan A= Perpendicular/Base =BC/AB

cot A= Base/Perpendicular=AB/BC

*Notice that each ratio in the right-hand column is the inverse, or the reciprocal, of the ratio in the left-hand column.*

The reciprocal of sin A is cosec A ; and vice-versa.

The reciprocal of cos A is sec A

And the reciprocal of tan A is cot A

**These are valid for acute angles.**

We can define tan A = sin A/cos A

And Cot A =cos A/ Sin A

**Important Note**

Since the hypotenuse is the longest side in a right triangle, the value of

sin A or cos A is always less than 1 (or, in particular, equal to 1).

Similarly we can have define these for angle $C$

We can define the trigonometric ratios for angle $C$ as

sin C= Perpendicular/Hypotenuse =AB/AC

cosec C= Hypotenuse/Perpendicular =AC/ABB

cos C= Base/Hypotenuse =BC/AC

sec C= Hypotenuse/Base=AC/BC

tan A= Perpendicular/Base =AB/BC

cot A= Base/Perpendicular=BC/AB

We can find the values of trigonometric ratio’s various angle

We know that for Angle A, the complementary angle is 90 – A

In a right angle triangle ABC

A+B+C=180

Now B=90

So A +C =90

Or C=90-A

We have see in Previous section the value for trigonometric ratios for angle $C$

sin C= Perpendicular/Hypotenuse =AB/AC

cosec C= Hypotenuse/Perpendicular =AC/ABB

cos C= Base/Hypotenuse =BC/AC

sec C= Hypotenuse/Base=AC/BC

tan C= Perpendicular/Base =AB/BC

cot C= Base/Perpendicular=BC/AB

This can be rewritten as

sin (90-A) =AB/AC

cosec (90-A) =AC/AB

cos (90-A) =BC/AC

sec (90-A)=AC/BC

tan (90-A)=AB/BC

cot( 90-A) =BC/AB

Also we know that

sin A=BC/AC

cosec A= AC/BC

cos A= AB/AC

sec A =AC/AB

tan A =BC/AB

cot A =AB/BC

*From both of these, we can easily make it out*

**Sin (90-A) =cos(A)**

**Cos(90-A) = sin A**

**Tan(90-A) =cot A**

**Sec(90-A)= cosec A**

**Cosec (90-A) =sec A**

**Cot(90- A) =tan A**

Sin^{2} A + cos^{2} A =0

1 + tan^{2} A =sec^{2} A

1 + cot^{2} A =cosec^{2} A

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