- 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

- Trignometry worksheet
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- trigonometry Worksheet-1
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- trigonometry Worksheet-2
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- trigonometry Proof questions
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- trigonometry Questions

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

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

We can define tan A = sin A/cos A

And Cot A =cos A/ Sin A

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).

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

sin C= Perpendicular/Hypotenuse =AB/AC

cosec C= Hypotenuse/Perpendicular =AC/AB

cos C= Base/Hypotenuse =BC/AC

sec C= Hypotenuse/Base=AC/BC

tan C= Perpendicular/Base =AB/BC

cot C= Base/Perpendicular=BC/AB

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

State whether the following are true or false. Justify your answer.

(i) The value of tan A is always less than 1.

(ii) sec A =12/5 for some value of angle A.

(iii) cos A is the abbreviation used for the cosecant of angle A.

(iv) tan A is the product of tan and A.

(v) sin ? =5/3 for some angle

i) False . The value of tan A increase from 0 to infinity

ii) True . The value of sec A increase from 1 to infinity

iii) False .Cos A is the abbreviation used for the cosine of angle A

iv) False .cot A is one symbol. We cannot separate it

v) False. The value of sin ? always lies between 0 and 1 and 5/3 > 1

The value of (sin30 + cos30) – (sin60 + cos60) is (A) – 1 (B) 0 (C) 1 (D) 2

Answer (B)

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

We have studied pythagorus theorem in earliar classes which states that for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two side

If a is the hypthonues and b and c are other two sides,then

a

This same theorem can be used to proved the below trigonometric identities

Sin

1 + tan

1 + cot

1) Learn well the formulas for Trigonometric identities, trigonometric ratios,reciprocals The better you know the basic identities, the easier it will be to recognise what is going on in the problems. 2) Generally RHS( Right hand side) would be more complex. So start from there and simplify it to the same form as LHS(Left hand side) 3) It becomes many times easy, if Convert all sec, csc, cot, and tan to sin and cos. Most of this can be done using the quotient and reciprocal identities. 4) If you see power 2 or more, it will involve using the below identities mostly Sin

1 + tan

1 + cot

5) Once you get the hang of it, you will begin to see patterns and it will be easy to solve these Trigonometric identities Problems 6) Practice and Practice. You will soon start figuring out the equation and there symmetry to resolve them fast

Prove that (sin

L.H.S. = (sin

= [(sin

= (sin

[Because sin

= 2sin

= 2 = RHS

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