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Activity :

1. Construct a table of the following trig onometric formulae for easy memorizing.

θ

θ

sin

1

cosec

θ

θ

cos

1

sec

θ

θ

cot

1

tan

θ

θ

θ

cos

sin

tan

θ

θ

θ

sin

cos

cot

sin^2 θcos^2 θ 1

sec^2 θ 1 tan^2 θ

cosec^2 θ 1 cot^2 θ

Example 1. If
3

4

tanA , find the other trigonometric ratios of the angle A.

Solution : Given that,
3

4

tanA.

So, opposite side of the angle A = 4, adjacent side = 3

hypotenuse = 42  32 25 5

Therefore,, sinA=
5

4

,cosA=

5

3

,cotA=

4

3

cosecA=

4

5

, secA=

3

5

.

Example 2. ‘B is the right angle of a right angled triangle ABC. If
4

3

tanA ,

verify the truth of 2sinAcosA = 1.

Solution : Given that,
4

3

tanA ,

So, opposite side of the angle A= 4, adjacent side = 3

hypotenuse = 42  32 5 5

so,
5

4

sinA ,

4

3

cosA

Hence, 2 sinAcosA= 2
5

4

˜

5

3

˜ =

25

24

z 1

Therefore, 2sinAcosA= 1 is a false statement.

Example 3. ‘B is a right angle of a right angled triangle ABC. If tanA 1 , verify

the justification of 2 sinAcosA 1.